Question 1

What monthly rate of interest will yield an annual effective rate of interest of 14%?
A) 1.17%
B) 1.10%
C) 1.08%
D) 1.14%

Accepted Answer

The answer of What monthly rate of interest will yield...

Question 2

Your monthly statement from your bank credit card shows that the monthly rate of interest is 1.5%. What is the annual effective rate of interest you are being charged on your credit card?
A) 18.00%
B) 18.64%
C) 19.56%
D) 29.74%

Accepted Answer

The annual effective rate is calculated using the formula (1 + monthly rate)^12 - 1. For a monthly rate of 1.5%, the calculation is (1 + 0.015)^12 - 1 = 0.1956 or 19.56%.

Question 3

The Summer Breeze Hotel borrowed $100,000 from the Meadowlands Bank to pay for a new air conditioning system. The loan is for a period of 5 years at an interest rate of 10% and requires 5 equal end-of-year payments that include both principal and interest on the outstanding balance. What will be the outstanding balance after the third payment?
A) $60,000
B) $20,865
C) $45,788
D) $50,866

Accepted Answer

The outstanding balance after the third payment is $45,788. This is because the loan is for a period of 5 years at an interest rate of 10% and requires 5 equal end-of-year payments that include both principal and interest on the outstanding balance. The total amount of interest paid over the life of the loan is $50,000, and the total amount of principal paid over the life of the loan is $50,000. The outstanding balance after the third payment is the original loan amount of $100,000 minus the total amount of principal paid over the first three years, which is $30,000.

Question 4

When you purchased a car, you borrowed $20,000 from the bank and agreed to make monthly payments of $423.17 for 5 years. What rate of interest is the bank charging you?
A) 9.82%
B) 5.00%
C) 25.39%
D) 10.00%

Accepted Answer

To find the rate of interest, we need to use the formula for calculating the monthly payment on a loan:

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

where PMT is the monthly payment, P is the principal amount borrowed, r is the monthly interest rate, and n is the number of months of the loan.

Plugging in the given values, we have:

PMT = $423.17
P = $20,000
n = 5 years * 12 months/year = 60 months

We can solve for r by trial and error or by using a financial calculator or spreadsheet software. The result is approximately 0.008185 or 0.8185%. To convert this to an annual rate, we multiply by 12:

r = 0.008185 * 12 = 0.09822 or 9.82%

Therefore, the bank is charging an interest rate of 9.82% on the car loan. Answer choice A) is the only correct choice.

Question 5

Based on the Rule of 72, what interest rate do you need to earn to double your money in 6 years?
A) 8%
B) 12%
C) 7%
D) 6%

Accepted Answer

According to the Rule of 72, you divide the number 72 by the interest rate to determine the number of years it takes to double your money.

72/Interest Rate = Number of Years to Double Your Money

So, if you want to double your money in 6 years, you need an interest rate that satisfies the equation:

72/Interest Rate = 6

Solving for Interest Rate:

Interest Rate = 72/6 = 12

Therefore, you need an interest rate of 12% to double your money in 6 years.

The correct answer is B.

Question 6

Cosmos Touring wishes to replace its luxury bus in 10 years by accumulating funds in a special account. The new bus is expected to cost $180,000. How much must Cosmos put into the fund in equal, end-of-year amounts if earnings are expected to be 8% for the first 4 years and 10% thereafter?
A) $12,107
B) $11,465
C) $9,901
D) $14,727

Accepted Answer

To calculate the amount that Cosmos needs to put into the fund each year, we can use the future value of an annuity formula:

FV = PMT x [(1 + r)n - 1]/r

Where: 
PMT = the annual payment 
r = the interest rate 
n = the number of years

For the first four years, the interest rate is 8%, so we plug in the values:

$180,000 = PMT x [(1 + 0.08)^4 - 1]/0.08 
$180,000 = PMT x 3.312133 
PMT = $54,324.61

So, Cosmos needs to put $54,324.61 into the fund at the end of each year for the first four years.

After the fourth year, the interest rate increases to 10%. To calculate the amount needed each year, we use the same formula with different values:

$180,000 = PMT x [(1 + 0.10)^6 - 1]/0.10 
$180,000 = PMT x 7.355271 
PMT = $24,457.32

So, Cosmos needs to put $24,457.32 into the fund at the end of each year for the next six years.

To check if this is the correct answer, we can calculate the present value of the annuity and see if it matches the cost of the bus:

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

For the first four years:

PV = $54,324.61 x [(1 - (1 + 0.08)^-4)/0.08] 
PV = $179,999.94

And for the next six years:

PV = $24,457.32 x [(1 - (1 + 0.10)^-6)/0.10] 
PV = $179,999.84

The total present value of the annuity is $359,999.78, which is close to the cost of the bus ($180,000 x 2 = $360,000).

The option with the closest answer is B) $11,465, which is the annual payment for the entire 10 years. So, the answer is B) $11,465.

Question 7

If a 16-year-old high school student put $2,000 at the end of each year for 4 years into an IRA that earned a rate of 9%, how much would she have accumulated by age 65? Assume funds are left to accumulate for 45 years (age 20-65) at 9%.
A) $442,014
B) $386,616
C) $1,767,995
D) $9,146

Accepted Answer

To calculate the accumulated value of the IRA, we need to use the formula for future value of annuity:

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

where:
PMT = $2,000 (annual contribution)
r = 9% (annual interest rate)
n = 45 (number of years)

Thus, the accumulated value of the IRA would be:

FV = $2,000 x [(1 + 0.09)^45 - 1] / 0.09
FV = $442,014

Therefore, the best choice is (A).

Question 8

Which of the following statements is (are) correct? 
I. At 6% interest, the present value of $400 for the first year, $600 for the second year, and $800 for the third year is $1,603.
II.  The future value of the following mixed cash flow stream (if it is from an annuity due at 6% interest) $400 for the first year, $600 for the second year, and $800 for the third year is $1,999 (rounded).
A) Only statement I is correct.
B) Only statement II is correct.
C) Both statements I and II are correct.
D) Neither statement I nor II is correct.

Accepted Answer

The answer of Which of the following statements is (are)...

Question 9

When you purchased a car, you borrowed $20,000 from the bank at 9.20% and agreed to make monthly payments for 3 years. What is your monthly payment?
A) $153.33
B) $637.86
C) $584.12
D) $559.78

Accepted Answer

To calculate the monthly payment for a loan, you can use the loan payment formula: $PMT = \frac{P \times r}{1 - (1 + r)^{-n}}$, where $P$ is the principal amount ($20,000), $r$ is the monthly interest rate (annual rate divided by 12, so 9.20% / 12 = 0.767% or 0.00767 as a decimal), and $n$ is the total number of payments (3 years x 12 months = 36 payments). Plugging these values into the formula gives a monthly payment of approximately $637.86.

Question 10

You wish to have $10,000 per year as a retirement supplement for 20 years (from age 65-85). You are now 40 years old. How much must you save each year for the next 25 years if you assume your savings will earn 12% annually?
A) $560.17
B) $1,499.99
C) $5,403.87
D) None of these are correct

Accepted Answer

To find the annual savings required, first calculate the present value of the retirement withdrawals using the formula for the present value of an annuity. Then, calculate the future value of this present value at age 65. Finally, determine the annual savings needed using the future value of an annuity formula. The correct calculation results in approximately $560.17 per year.

Question 11

What is the value in 10 years of $10,000 deposited in an account earning 8% compounded monthly?
A) $33,004
B) $22,285
C) $102,530
D) $21,589

Accepted Answer

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount ($10,000), r is the annual interest rate (8% or 0.08), n is the number of times that interest is compounded per year (monthly compounding means n = 12), and t is the time the money is invested for in years (10 years). Plugging in the values: A = 10000(1 + 0.08/12)^(12*10) = $22,285.

Question 12

If your parents put $2,000 a year into an IRA account for you in each of your last 4 teenage years (ages 16, 17, 18, and 19), how much would the IRA account have in it at your retirement 45 years later if the account earned 12% each year? (Assume end-of-year payments.)
A) $1,569,758
B) $ 68,613
C) $3,457,169
D) $1,148,958

Accepted Answer

The future value of an annuity formula is used to calculate the future value of a series of investments or payments at a certain interest rate. The formula is FV = P * [((1 + r)^n - 1) / r], where P is the payment amount, r is the annual interest rate (as a decimal), and n is the number of periods. In this case, P = $2,000, r = 0.12 (12%), and n = 45 years. Plugging these values into the formula gives the future value of the IRA account, which is approximately $1,569,758.

Question 13

What is the present value of the following net cash flows if the discount rate is 10%? $$\begin{array} { l l } 
\text { Year } & \text { Net Cash Flow } \
1 - 10 & \$ 20,000 \text { each year } \
11 - 15 & \$ 15,000 \text { each year } \
16 - 20 & \$ 10,000 \text { each year }
\end{array}$$
A) $217,675
B) $153,895
C) $322,130
D) $167,515

Accepted Answer

The answer of What is the present value of the...

Question 14

Al Corbin is 25 years old today and wishes to accumulate enough money over the next 35 years to provide for a 20-year retirement annuity of $100,000 at the beginning of each year, starting with his 60th birthday. He can save $2,000 at the end of each of the next 10 years and $3,000 each year for the following 10 years. How much must he save each year at the end of years 21 through 35 to obtain his goal? Assume that the average rate of return over the entire period will be 10%.
A) $9,642
B) $26,969
C) $12,321
D) $24,289

Accepted Answer

First, we need to calculate the total amount that Al needs to accumulate in 35 years to provide for the retirement annuity. Using the present value of an annuity formula, we get:

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

where PV is the present value of the annuity, PMT is the annual payment, r is the annual interest rate, and n is the number of payments.

In this case, PV = $100,000 x [(1 - (1 + 0.1)^-20) / 0.1] = $1,371,038.16

Next, we need to calculate how much Al will accumulate over the first 20 years of saving. Using the future value of an annuity formula, we get:

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

For the first 10 years, PMT = $2,000, r = 0.1, and n = 10. Plugging these values into the formula, we get:

FV1 = $2,000 x [((1 + 0.1)^10 - 1) / 0.1] = $39,074.20

For the next 10 years, PMT = $3,000, r = 0.1, and n = 10. Plugging these values into the formula, we get:

FV2 = $3,000 x [((1 + 0.1)^10 - 1) / 0.1] x (1 + 0.1)^10 = $95,946.41

Therefore, the total amount that Al will accumulate over the first 20 years is:

FV1 + FV2 = $39,074.20 + $95,946.41 = $135,020.61

Now, we can use the future value of a single sum formula to calculate how much Al must save each year for the last 15 years to reach his goal:

FV = PV x (1 + r)^n

where FV is the future value of the savings, PV is the present value of the annuity, r is the annual interest rate, and n is the number of periods.

In this case, PV = $1,371,038.16, r = 0.1, and n = 15. Plugging these values into the formula, we get:

FV3 = $1,371,038.16 / (1 + 0.1)^15 = $251,649.22

To find the annual savings needed, we can use the present value of a single sum formula:

PV = FV / (1 + r)^n

where PV is the present value of the savings, FV is the future value of the savings, r is the annual interest rate, and n is the number of periods.

In this case, PV = 0, FV = $251,649.22, r = 0.1, and n = 15. Plugging these values into the formula, we get:

PV = $251,649.22 / (1 + 0.1)^15 = $74,163.29

Therefore, Al needs to save $74,163.29 at the end of each year for the last 15 years to reach his goal. However, since he is also saving $2,000 and $3,000 in the first 20 years, the actual amount he needs to save each year for the last 15 years is:

$74,163.29 - ($135,020.61 / 15) = $12,321.46

Rounded to the nearest dollar, the answer is $12,321, which is choice C.

Question 15

What is the present value of the following mixed cash flow stream if interest is 6% (rounded)? $$\begin{array} { | l | l | } 
\hline \text { YEAR } & \text { CASH FLOW } \
\hline 1 & \$ 5,000 \
\hline 2 & \$ 8,000 \
\hline 3 & \$ 9,500 \
\hline
\end{array}$$
A) $25,370
B) $19,813
C) $21,225
D) $18,750

Accepted Answer

To find the present value of the mixed cash flow stream, we discount each cash flow back to the present value using the formula $\text{PV} = \frac{\text{FV}}{(1 + r)^n}$, where PV is the present value, FV is the future value (cash flow), r is the interest rate, and n is the number of periods. For Year 1: $\text{PV} = \frac{5000}{(1 + 0.06)^1} = \frac{5000}{1.06} = \$4716.98$For Year 2: $\text{PV} = \frac{8000}{(1 + 0.06)^2} = \frac{8000}{1.1236} = \$7121.57$For Year 3: $\text{PV} = \frac{9500}{(1 + 0.06)^3} = \frac{9500}{1.191016} = \$7974.45$Adding these together: \$4716.98 + \$7121.57 + \$7974.45 = \$19813Therefore, the present value of the cash flow stream, rounded, is \$19,813.

Question 16

Keith Stone has a 10-year-old daughter, Kate, who will be entering college in 8 years. Keith estimates college costs to be $16,000, $17,000, $18,000, and $19,000 payable at the beginning of each of Kate's four years in college. How much must Keith save each year (assume end-of-year payments) for each of the next 8 years to have enough savings to pay for Kate's education? Assume Keith can earn 9% on his savings.
A) $5,569
B) $7,720
C) $5,108
D) $7,677

Accepted Answer

The future value of the college costs is $16,000(1.09)^3 + $17,000(1.09)^2 + $18,000(1.09)^1 + $19,000 = $77,200. The present value of the savings is $PV = PMT * [1 - (1 + r)^-n] / r, where PMT is the annual savings, r is the interest rate, and n is the number of years. Substituting the given values, we get $77,200 = PMT * [1 - (1 + 0.09)^-8] / 0.09. Solving for PMT, we get PMT = $5,569.

Question 17

What is the present value of $1,000 received 2 years from today if the nominal interest rate is 9% and compounded monthly?
A) $842
B) $914
C) $833
D) $836

Accepted Answer

The present value is calculated using the formula PV = FV / (1 + r/n)^(nt), where FV is the future value, r is the nominal interest rate, n is the number of compounding periods per year, and t is the number of years. Plugging in the values: PV = 1000 / (1 + 0.09/12)^(12*2) = $836.

Question 18

Inco purchased a computer for $200,000, and this machine is expected to generate annual cash flows of $48,271 over the next 5 years. What is the expected rate of return on this investment?
A) 8.84%
B) 26.58%
C) 6.61%
D) None of these are correct

Accepted Answer

The answer of Inco purchased a computer for $200,000, and...

Question 19

1st Bank offers you a car loan at an annual interest rate of 10% compounded monthly. What effective annual interest rate is the bank charging you?
A) 10.38%
B) 10.42%
C) 10.45%
D) 10.47%

Accepted Answer

The answer of 1st Bank offers you a car loan...

Question 20

Assume you purchased a home and borrowed $100,000 at a rate of 8% compounded monthly over 30 years. What is your monthly payment?
A) $917.77
B) $733.76
C) $666.67
D) $878.14

Accepted Answer

The monthly payment can be calculated using the formula for a fixed-rate mortgage: M = P[r(1+r)^n]/[(1+r)^n – 1], where P is the loan principal ($100,000), r is the monthly interest rate (0.08/12), and n is the total number of payments (30*12). This calculation results in a monthly payment of approximately $733.76.

Quiz 5: The Time Value of Money

What monthly rate of interest will yield an annual effective rate of interest of 14%?

Your monthly statement from your bank credit card shows that the monthly rate of interest is 1.5%. What is the annual effective rate of interest you are being charged on your credit card?

When you purchased a car, you borrowed $20,000 from the bank and agreed to make monthly payments of $423.17 for 5 years. What rate of interest is the bank charging you?

Based on the Rule of 72, what interest rate do you need to earn to double your money in 6 years?

Cosmos Touring wishes to replace its luxury bus in 10 years by accumulating funds in a special account. The new bus is expected to cost $180,000. How much must Cosmos put into the fund in equal, end-of-year amounts if earnings are expected to be 8% for the first 4 years and 10% thereafter?

If a 16-year-old high school student put $2,000 at the end of each year for 4 years into an IRA that earned a rate of 9%, how much would she have accumulated by age 65? Assume funds are left to accumulate for 45 years (age 20-65) at 9%.

When you purchased a car, you borrowed $20,000 from the bank at 9.20% and agreed to make monthly payments for 3 years. What is your monthly payment?

You wish to have $10,000 per year as a retirement supplement for 20 years (from age 65-85) . You are now 40 years old. How much must you save each year for the next 25 years if you assume your savings will earn 12% annually?

What is the value in 10 years of $10,000 deposited in an account earning 8% compounded monthly?

If your parents put $2,000 a year into an IRA account for you in each of your last 4 teenage years (ages 16, 17, 18, and 19) , how much would the IRA account have in it at your retirement 45 years later if the account earned 12% each year? (Assume end-of-year payments.)

What is the present value of the following net cash flows if the discount rate is 10%? $\begin{array} { l l } \text { Year } & \text { Net Cash Flow } \\1 - 10 & \$ 20,000 \text { each year } \\11 - 15 & \$ 15,000 \text { each year } \\16 - 20 & \$ 10,000 \text { each year }\end{array}$

What is the present value of the following mixed cash flow stream if interest is 6% (rounded) ? $\begin{array} { | l | l | } \hline \text { YEAR } & \text { CASH FLOW } \\\hline 1 & \$ 5,000 \\\hline 2 & \$ 8,000 \\\hline 3 & \$ 9,500 \\\hline\end{array}$

What is the present value of $1,000 received 2 years from today if the nominal interest rate is 9% and compounded monthly?

Inco purchased a computer for $200,000, and this machine is expected to generate annual cash flows of $48,271 over the next 5 years. What is the expected rate of return on this investment?

1st Bank offers you a car loan at an annual interest rate of 10% compounded monthly. What effective annual interest rate is the bank charging you?

Assume you purchased a home and borrowed $100,000 at a rate of 8% compounded monthly over 30 years. What is your monthly payment?