Question 1

Find the present value of the decreasing annuity necessary to fund a withdrawal of $100 per month for 20 years, if the annuity earns 3% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​

Accepted Answer

This problem requires us to find the present value of a decreasing annuity. Since the payments are made at the end of each month, we need to use the monthly interest rate and the number of periods in months. Using the formula for the present value of a decreasing annuity, we get:

PV = (P/i) * (1 - (1 + i)^(-n)),

where PV is the present value, P is the monthly payment, i is the monthly interest rate, and n is the number of periods.

Plugging in the given values, we get:

PV = (100/0.0025) * (1 - (1 + 0.0025)^(-240))
PV = $18,031.09 (rounded to the nearest cent)

Therefore, the best choice is B.

Question 2

Find the periodic withdrawal for an annuity of $240,000 at 6%, paid out quarterly for 25 years. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

Accepted Answer

To find the periodic withdrawal for an annuity, we use the annuity formula: $PMT = \frac{PV}{\frac{1 - (1 + r)^{-n}}{r}}$, where PV = present value of the annuity ($240,000), r = periodic interest rate (6% annually or 0.06/4 = 0.015 quarterly), and n = total number of periods (25 years * 4 quarters/year = 100 quarters). Plugging these values into the formula gives the periodic withdrawal amount, which is closest to option A.

Question 3

Find the amount accumulated in the increasing annuity of $2,500 deposited quarterly for 25 years at 4% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round answer to the nearest cent. ​

Accepted Answer

D

Question 4

Determine the selling price, per $1,000 maturity value, of a 10-year, 4.885% bond, with a yield of 4.890%. (Assume twice-yearly interest payments.) Round your answer to the nearest cent. ​

Accepted Answer

Step 1: Calculate the semi-annual coupon payment 
Coupon rate = 4.885% ÷ 2 = 2.4425%
Semi-annual coupon payment = $1,000 × 2.4425% = $24.425

Step 2: Calculate the number of semi-annual periods 
10 years × 2 semi-annual periods per year = 20 semi-annual periods

Step 3: Calculate the present value of the semi-annual payments 
PV of semi-annual payments = $24.425 × [1 – (1 + 4.890%/2)^(-20)] ÷ (4.890%/2) 
= $436.78

Step 4: Calculate the present value of the final payment 
PV of final payment = $1,000 ÷ (1 + 4.890%/2)^20 
= $613.83

Step 5: Calculate the selling price 
Selling price = PV of semi-annual payments + PV of final payment 
= $436.78 + $613.83 
= $1,050.61

Step 6: Calculate the selling price per $1,000 maturity value 
Selling price per $1,000 maturity value = Selling price ÷ $1,000 × 100% 
= $1,050.61 ÷ $1,000 × 100% 
= 105.061%

Rounded to the nearest cent, the selling price per $1,000 maturity value is $999.61. Thus, the best choice is A.

Question 5

Find the periodic withdrawal for an annuity of $75,000 at 4%, paid out quarterly for 25 years. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

Accepted Answer

To find the periodic withdrawal for an annuity, we use the annuity formula: $PMT = PV \times \frac{r}{1 - (1 + r)^{-n}}$, where PMT is the periodic payment, PV is the present value of the annuity, r is the periodic interest rate, and n is the total number of payments. Given a $75,000 annuity at 4% annual interest, paid quarterly for 25 years, we first convert the annual interest rate to a quarterly rate (4% / 4 = 1%) and the number of years to the number of quarterly periods (25 years * 4 = 100 quarters). Plugging these values into the formula gives a PMT value, which, when calculated correctly, is closest to the option D, $1,189.93.

Question 6

Find the present value of a decreasing annuity necessary to fund withdrawals of $1,100 per month for 10 years, if the annuity earns 6% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​

Accepted Answer

The answer of Find the present value of a decreasing...

Question 7

Determine the monthly payment necessary to accumulate $30,000 in a fund paying 6% per year, compounded monthly, for 8 years. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​

Accepted Answer

The correct answer is A. $244.24 per month.The formula for the future value of an annuity is:FV = PMT * (((1 + r/n)^(n*t)) - 1) / (r/n))where:PMT is the monthly paymentFV is the future valuer is the annual interest raten is the number of compounding periods per yeart is the number of yearsIn this case, we have:FV = $30,000r = 6% = 0.06n = 12 (monthly compounding)t = 8Plugging these values into the formula, we get:$30,000 = PMT * (((1 + 0.06/12)^(12*8)) - 1) / (0.06/12))Solving for PMT, we get:PMT = $244.24

Question 8

Find the periodic withdrawal for an annuity containing $275,000 at 6%, paid out monthly for 30 years. (Assume end-of-period deposits and compounding at the same intervals as deposits). Round your answer to the nearest cent.

Accepted Answer

The answer of Find the periodic withdrawal for an annuity...

Question 9

Find the amount accumulated in the increasing annuity of $200 deposited monthly for 5 years at 3% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​

Accepted Answer

To find the amount accumulated in an increasing annuity, we use the future value of an annuity formula adjusted for monthly deposits and compounding. The formula for the future value of an annuity when compounding and deposits are made at the same frequency is $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $P$ is the payment amount per period, $r$ is the interest rate per period, and $n$ is the total number of payments. For monthly deposits at an annual interest rate, $r = \frac{0.03}{12}$ and $n = 5 \times 12 = 60$. Plugging in the values: $FV = 200 \times \frac{(1 + \frac{0.03}{12})^{60} - 1}{\frac{0.03}{12}}$, calculating this gives a future value close to $12,929.34, which matches option C.

Question 10

Find the amount accumulated in an increasing annuity in which $100 is deposited monthly for 20 years at 5% per year in an account containing $10,000 at the start. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​

Accepted Answer

We can solve this problem using the formula for the future value of an increasing annuity:

FV = Pmt x [(1 + r)^n - 1]/r + PV x (1 + r)^n

where:
- Pmt = the monthly deposit amount = $100
- r = the monthly interest rate = 5% / 12 = 0.00417
- n = the number of months = 20 years x 12 = 240
- PV = the present value = $10,000

Plugging in these values, we get:

FV = $100 x [(1 + 0.00417)^240 - 1]/0.00417 + $10,000 x (1 + 0.00417)^240
   = $100 x 319.872 + $10,000 x 2.653297
   = $68,229.77

So the answer is A.

Question 11

Determine the periodic payment for a loan of $25,000 borrowed at 6% for 7 years, with monthly payments. Round your answer to the nearest cent. ​

Accepted Answer

To solve for the periodic payment, we can use the formula for mortgage or loan payments:

P = (PV * r) / (1 - (1+r)^(-n))

Where P is the periodic payment, PV is the present value of the loan, r is the monthly interest rate (6%/12 = 0.005), and n is the total number of payments (7*12 = 84).

Plugging in the numbers, we get:

P = (25,000 * 0.005) / (1 - (1+0.005)^(-84))
P = 365.21

So the periodic payment for this loan is $365.21, which is closest to answer choice A.

Question 12

Find the present value of a decreasing annuity necessary to fund withdrawals of $2,500 per quarter for 20 years, if the annuity earns 4% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits). Round your answer to the nearest cent.

Accepted Answer

The present value of a decreasing annuity can be calculated using the formula for the present value of an annuity due to the withdrawals happening at the end of each period. Given the quarterly withdrawals of $2,500 for 20 years at an annual interest rate of 4%, compounded quarterly, the correct calculation leads to the present value of approximately $137,220.52, making option A the correct answer.

Question 13

Find the periodic withdrawal for an annuity of $140,000 at 5%, paid out monthly for 17 years. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

Accepted Answer

The periodic withdrawal can be calculated using the formula for the annuity payment: $ PMT = \frac{P \cdot r}{1 - (1 + r)^{-n}} $, where $ P = 140,000 $, $ r = \frac{0.05}{12} $, and $ n = 17 \times 12 $. Solving this gives approximately $1,020.12.

Question 14

Determine the monthly payment necessary to accumulate $30,000 in a fund paying 6% per year, compounded monthly, for 8 years. Assume end-of-period deposits and compounding at the same intervals as deposits. Round the answer to the nearest cent. ​

Accepted Answer

To find the monthly payment, use the future value of an annuity formula: FV = Pmt * [(1 + r)^nt - 1] / r. Here, FV = $30,000, r = 0.06/12, n = 8*12. Solving for Pmt gives approximately $244.24.

Question 15

Find the amount accumulated in the increasing annuity of $150 deposited monthly for 15 years at 5% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​

Accepted Answer

Using the formula for the future value of an increasing annuity:

FV = Pmt * [((1+r)^n - 1)/r] + PV * (1+r)^n

where:
Pmt = monthly deposit amount = $150
r = annual interest rate = 5% / 12 = 0.00416667
n = number of periods = 15 years * 12 months/year = 180 months
PV = present value (initial deposit) = $0

Plugging in the values, we get:

FV = $150 * [((1+0.00416667)^180 - 1)/0.00416667] + $0 * (1+0.00416667)^180
FV = $40,093.34

Therefore, the amount accumulated in the increasing annuity is $40,093.34. The best choice is B.

Question 16

Determine the quarterly payment necessary to accumulate $65,000 in a fund paying 8% per year, compounded quarterly, for 10 years. Assume end-of-period deposits and compounding at the same intervals as deposits. Round the answer to the nearest cent. ​

Accepted Answer

The answer of Determine the quarterly payment necessary to accumulate...

Question 17

While shopping for a car loan, you get the following offers: Solid Savings & Loan is willing to loan you $25,000 at 13% interest for 5 years. Fifth Federal Bank & Trust will loan you the $25,000 at 7% for 6 years. Both require monthly payments. You can afford $500 per month. Which loan, if either, can you take

Accepted Answer

To determine the best choice, we need to calculate the total amount paid for each loan.

For Solid Savings & Loan:

- Interest = 13/100 * $25,000 * 5 = $16,250 
- Total amount paid = $25,000 + $16,250 = $41,250

For Fifth Federal Bank & Trust:

- Interest = 7/100 * $25,000 * 6 = $10,500 
- Total amount paid = $25,000 + $10,500 = $35,500

Since the monthly payment is capped at $500, it is not possible to take the Solid Savings & Loan loan as the monthly payment would be $687.50 which is beyond our limit.

On the other hand, we can take the Fifth Federal Bank & Trust loan as the monthly payment would be $522.22 which is within our limit.

Therefore, the best choice is to take the loan from Fifth Federal Bank & Trust.

Question 18

Determine the periodic payment for a loan of $200,000 borrowed at 3% for 15 years, with monthly payments. Round your answer to the nearest cent. ​

Accepted Answer

The periodic payment can be calculated using the formula for an amortizing loan: P = [r*PV] / [1 - (1 + r)^-n], where P is the monthly payment, r is the monthly interest rate (annual rate/12), PV is the present value or loan amount, and n is the total number of payments. For this loan, r = 0.03/12, PV = $200,000, and n = 15*12. Plugging these values into the formula gives a monthly payment of approximately $1,381.16.

Question 19

Find the amount accumulated in the increasing annuity of $2,500 deposited quarterly for 10 years at 5% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​

Accepted Answer

The answer of Find the amount accumulated in the increasing...

Question 20

Find the present value of the decreasing annuity necessary to fund a withdrawal of $1,500 per quarter for 20 years, if the annuity earns 3% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​

Accepted Answer

The answer of Find the present value of the decreasing...

Quiz 3: The Mathematics of Finance

Find the present value of the decreasing annuity necessary to fund a withdrawal of $100 per month for 20 years, if the annuity earns 3% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

Find the periodic withdrawal for an annuity of $240,000 at 6%, paid out quarterly for 25 years. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

Find the amount accumulated in the increasing annuity of $2,500 deposited quarterly for 25 years at 4% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round answer to the nearest cent.

Determine the selling price, per $1,000 maturity value, of a 10-year, 4.885% bond, with a yield of 4.890%. (Assume twice-yearly interest payments.) Round your answer to the nearest cent.

Find the periodic withdrawal for an annuity of $75,000 at 4%, paid out quarterly for 25 years. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

Find the present value of a decreasing annuity necessary to fund withdrawals of $1,100 per month for 10 years, if the annuity earns 6% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

Determine the monthly payment necessary to accumulate $30,000 in a fund paying 6% per year, compounded monthly, for 8 years. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

Find the periodic withdrawal for an annuity containing $275,000 at 6%, paid out monthly for 30 years. (Assume end-of-period deposits and compounding at the same intervals as deposits) . Round your answer to the nearest cent.

Find the amount accumulated in the increasing annuity of $200 deposited monthly for 5 years at 3% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

Find the amount accumulated in an increasing annuity in which $100 is deposited monthly for 20 years at 5% per year in an account containing $10,000 at the start. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

Determine the periodic payment for a loan of $25,000 borrowed at 6% for 7 years, with monthly payments. Round your answer to the nearest cent.

Find the present value of a decreasing annuity necessary to fund withdrawals of $2,500 per quarter for 20 years, if the annuity earns 4% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits) . Round your answer to the nearest cent.

Find the periodic withdrawal for an annuity of $140,000 at 5%, paid out monthly for 17 years. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

Determine the monthly payment necessary to accumulate $30,000 in a fund paying 6% per year, compounded monthly, for 8 years. Assume end-of-period deposits and compounding at the same intervals as deposits. Round the answer to the nearest cent.

Find the amount accumulated in the increasing annuity of $150 deposited monthly for 15 years at 5% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

Determine the quarterly payment necessary to accumulate $65,000 in a fund paying 8% per year, compounded quarterly, for 10 years. Assume end-of-period deposits and compounding at the same intervals as deposits. Round the answer to the nearest cent.

Determine the periodic payment for a loan of $200,000 borrowed at 3% for 15 years, with monthly payments. Round your answer to the nearest cent.

Find the amount accumulated in the increasing annuity of $2,500 deposited quarterly for 10 years at 5% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

Find the present value of the decreasing annuity necessary to fund a withdrawal of $1,500 per quarter for 20 years, if the annuity earns 3% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

Quiz 3: The Mathematics of Finance

Find the present value of the decreasing annuity necessary to fund a withdrawal of $100 per month for 20 years, if the annuity earns 3% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​

Find the periodic withdrawal for an annuity of $240,000 at 6%, paid out quarterly for 25 years. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

Find the amount accumulated in the increasing annuity of $2,500 deposited quarterly for 25 years at 4% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round answer to the nearest cent. ​

Determine the selling price, per $1,000 maturity value, of a 10-year, 4.885% bond, with a yield of 4.890%. (Assume twice-yearly interest payments.) Round your answer to the nearest cent. ​

Find the periodic withdrawal for an annuity of $75,000 at 4%, paid out quarterly for 25 years. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

Find the present value of a decreasing annuity necessary to fund withdrawals of $1,100 per month for 10 years, if the annuity earns 6% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​

Determine the monthly payment necessary to accumulate $30,000 in a fund paying 6% per year, compounded monthly, for 8 years. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​

Find the periodic withdrawal for an annuity containing $275,000 at 6%, paid out monthly for 30 years. (Assume end-of-period deposits and compounding at the same intervals as deposits) . Round your answer to the nearest cent.

Find the amount accumulated in the increasing annuity of $200 deposited monthly for 5 years at 3% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​

Find the amount accumulated in an increasing annuity in which $100 is deposited monthly for 20 years at 5% per year in an account containing $10,000 at the start. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​

Determine the periodic payment for a loan of $25,000 borrowed at 6% for 7 years, with monthly payments. Round your answer to the nearest cent. ​

Find the present value of a decreasing annuity necessary to fund withdrawals of $2,500 per quarter for 20 years, if the annuity earns 4% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits) . Round your answer to the nearest cent.

Find the periodic withdrawal for an annuity of $140,000 at 5%, paid out monthly for 17 years. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

Determine the monthly payment necessary to accumulate $30,000 in a fund paying 6% per year, compounded monthly, for 8 years. Assume end-of-period deposits and compounding at the same intervals as deposits. Round the answer to the nearest cent. ​

Find the amount accumulated in the increasing annuity of $150 deposited monthly for 15 years at 5% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​

Determine the quarterly payment necessary to accumulate $65,000 in a fund paying 8% per year, compounded quarterly, for 10 years. Assume end-of-period deposits and compounding at the same intervals as deposits. Round the answer to the nearest cent. ​

Determine the periodic payment for a loan of $200,000 borrowed at 3% for 15 years, with monthly payments. Round your answer to the nearest cent. ​

Find the amount accumulated in the increasing annuity of $2,500 deposited quarterly for 10 years at 5% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​

Find the present value of the decreasing annuity necessary to fund a withdrawal of $1,500 per quarter for 20 years, if the annuity earns 3% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​

Find the present value of the decreasing annuity necessary to fund a withdrawal of $100 per month for 20 years, if the annuity earns 3% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

Find the amount accumulated in the increasing annuity of $2,500 deposited quarterly for 25 years at 4% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round answer to the nearest cent.

Determine the selling price, per $1,000 maturity value, of a 10-year, 4.885% bond, with a yield of 4.890%. (Assume twice-yearly interest payments.) Round your answer to the nearest cent.

Find the present value of a decreasing annuity necessary to fund withdrawals of $1,100 per month for 10 years, if the annuity earns 6% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

Determine the monthly payment necessary to accumulate $30,000 in a fund paying 6% per year, compounded monthly, for 8 years. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

Find the amount accumulated in the increasing annuity of $200 deposited monthly for 5 years at 3% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

Find the amount accumulated in an increasing annuity in which $100 is deposited monthly for 20 years at 5% per year in an account containing $10,000 at the start. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

Determine the periodic payment for a loan of $25,000 borrowed at 6% for 7 years, with monthly payments. Round your answer to the nearest cent.

Determine the monthly payment necessary to accumulate $30,000 in a fund paying 6% per year, compounded monthly, for 8 years. Assume end-of-period deposits and compounding at the same intervals as deposits. Round the answer to the nearest cent.

Find the amount accumulated in the increasing annuity of $150 deposited monthly for 15 years at 5% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

Determine the quarterly payment necessary to accumulate $65,000 in a fund paying 8% per year, compounded quarterly, for 10 years. Assume end-of-period deposits and compounding at the same intervals as deposits. Round the answer to the nearest cent.

Determine the periodic payment for a loan of $200,000 borrowed at 3% for 15 years, with monthly payments. Round your answer to the nearest cent.

Find the amount accumulated in the increasing annuity of $2,500 deposited quarterly for 10 years at 5% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.

Find the present value of the decreasing annuity necessary to fund a withdrawal of $1,500 per quarter for 20 years, if the annuity earns 3% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.