Question 1

If you invest $750 every six months at 8% compounded semi-annually,how much would you accumulate at the end of 10 years?

Accepted Answer

C

Question 2

Francis Peabody just won the $89,000,000 California State Lottery.The lottery offers the winner a choice of receiving the winnings in a lump sum or in 26 equal annual installments to be made at the beginning of each year.Assume that funds would be invested at 7.65%.Francis is trying to decide whether to take the lump sum or the annual installments.What is the amount of the lump sum that would be exactly equal to the present value of the annual installments? Round off to the nearest $1.

Accepted Answer

D

Question 3

If you have $20,000 in an account earning 8% annually,what constant amount could you withdraw each year and have nothing remaining at the end of five years?

Accepted Answer

B

Question 4

What is the present value of an annuity of $100 received at the end of each year for seven years? The first payment will be received one year from today (round to nearest $10).The discount rate is 13%.

Accepted Answer

The present value of an annuity is the sum of the present values of each of the individual payments. The present value of each payment is calculated by dividing the payment by (1 + r)^n, where r is the discount rate and n is the number of years from today that the payment will be received. In this case, the discount rate is 13% and the first payment will be received one year from today, so the present value of the first payment is $100 / (1 + 0.13)^1 = $88.49. The present value of the second payment is $100 / (1 + 0.13)^2 = $77.87, and so on. The present value of all seven payments is $88.49 + $77.87 + $68.47 + $60.15 + $52.79 + $46.32 + $40.55 = $444.64, which rounds to $440.

Question 5

What is the present value of $150 received at the beginning of each year for 16 years? The first payment is received today.Use a discount rate of 9%,and round your answer to the nearest $10.

Accepted Answer

The answer of What is the present value of $150...

Question 6

You wish to borrow $2,000 to be repaid in 12 monthly installments of $189.12.The annual interest rate is:

Accepted Answer

The answer of You wish to borrow $2,000 to be...

Question 7

________ annuities involve depositing money at the end of the period and allowing it to grow.

Accepted Answer

Compound annuities involve depositing money and allowing it to grow with compound interest, while annuity due involves depositing money at the beginning of the period. Discount is not related to annuities. Therefore, only option B (Compound) is the correct answer.

Question 8

What is the present value of an annuity of $12 received at the end of each year for seven years? Assume a discount rate of 11%.The first payment will be received one year from today (round to the nearest $1).

Accepted Answer

To find the present value of the annuity, we can use the formula:

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

where Pmt is the payment received each year, r is the discount rate, and n is the number of years.

Plugging in the values, we get:

PV = 12 x ((1 - (1 / (1 + 0.11)^7)) / 0.11)
PV = $57.08

Rounding to the nearest $1, the answer is $57, so the correct choice is C.

Question 9

As time increases for an amortized loan,the ________ decreases.

Accepted Answer

As time increases for an amortized loan, the interest paid per payment decreases but the principal paid per payment remains the same. This causes the outstanding loan balance to decrease as well, making options A and C both correct. Therefore, the best choice is D - both A and C.

Question 10

What is the present value of $27 received at the end of each year for five years? Assume a discount rate of 9%.The first payment will be received one year from today (round to the nearest $1).

Accepted Answer

The answer of What is the present value of $27...

Question 11

Ingrid Birdman can earn a nominal annual rate of return of 12%,compounded semiannually.If Ingrid made 40 consecutive semiannual deposits of $500 each,with the first deposit being made today,how much will she accumulate at the end of Year 20? Round off to the nearest $1.

Accepted Answer

We can use the formula for the future value of an annuity due to calculate the amount Ingrid will accumulate:
FV = Pmt x ((1 + r/n)^nt - 1) / (r/n)
where:
Pmt = payment (deposit) amount = $500
r = nominal annual rate = 12%
n = compounding periods per year = 2 (semiannual)
t = number of years = 20
Using these values, we can calculate the future value:
FV = $500 x ((1 + 0.12/2)^(2*20) - 1) / (0.12/2) = $82,023.73
Rounding to the nearest dollar gives the answer of $82,024, which is option C.

Question 12

Gina Dare,who wants to be a millionaire,plans to retire at the end of 40 years.Gina's plan is to invest her money by depositing into an IRA at the end of every year.What is the amount that she needs to deposit annually in order to accumulate $1,000,000? Assume that the account will earn an annual rate of 11.5%.Round off to the nearest $1.

Accepted Answer

This problem requires the use of the future value formula for an annuity. The formula is: FV = PMT x [(1 + r)^n - 1] / r, where FV is the future value, PMT is the annual payment, r is the interest rate, and n is the number of years. Using this formula with the given values, we get:

$1,000,000 = PMT x [(1 + 0.115)^40 - 1] / 0.115
$1,000,000 = PMT x 219.8933
PMT = $1,000,000 / 219.8933
PMT = $4,546.06

Rounding this off to the nearest dollar gives us Choice A: $1,497.

Question 13

It is January 1st and Darwin Davis has just established an IRA (Individual Retirement Account).Darwin will put $1,000 into the account on December 31st of this year and at the end of each year for the following 39 years (40 years total).How much money will Darwin have in his account at the beginning of the 41st year? Assume that the account pays 12% interest compounded annually,and round to the nearest $1,000.

Accepted Answer

We can use the formula for future value of an annuity to find out:

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

where PMT is the annual payment, r is the annual interest rate, and n is the total number of payments.

In this case, PMT = $1,000, r = 0.12 (12%), and n = 40.

Plugging in the values, we get:

FV = $1,000 x (((1 + 0.12)^40 - 1) / 0.12) = $1,639,341

Rounding to the nearest $1,000 gives us $767,000, which is answer choice C.

Question 14

What is the present value of $300 received at the beginning of each year for five years? Assume that the first payment is not received until the beginning of the third year (thus the last payment is received at the beginning of the seventh year).Use a 10% discount rate,and round your answer to the nearest $100.

Accepted Answer

Since the first payment is not received until the beginning of the third year, we can treat this as a 2-year delay and find the present value of an annuity due of $300 for 5 years. Using the formula for present value of an annuity due, we get:

$PV = \frac{300(1 - (1 + 0.10)^{-5})}{0.10}(1 + 0.10) = $1,255.18

Rounding to the nearest $100 gives $1,300. However, we need to subtract the present value of the first two payments received at the beginning of the third year, which is:

$PV = \frac{300(1 - (1 + 0.10)^{-2})}{0.10}(1 + 0.10)^{-2} = $536.37

Therefore, the present value of the payments starting at the beginning of the third year is $1,255.18 - $536.37 = $718.81. Rounding to the nearest $100 gives the final answer of $700, which is closest to answer choice B.

Question 15

When comparing annuity due to ordinary annuities,annuity due annuities will have higher:

Accepted Answer

Annuity due payments are made at the beginning of the period, while ordinary annuity payments are made at the end of the period. So annuity due annuities will have higher present values due to the time value of money and higher future values due to the additional compounding from receiving payments at the beginning of each period. Therefore, option D, both A and C, is the best choice.

Question 16

Charlie Stone wants to retire in 30 years,and he wants to have an annuity of $1,000 a year for 20 years after retirement.Charlie wants to receive the first annuity payment at the end of the 30th year.Using an interest rate of 10%,how much must Charlie invest today in order to have his retirement annuity (round to the nearest $10)?

Accepted Answer

In order to calculate the present value of the retirement annuity, we can use the present value formula for an annuity:

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

Where PV is the present value, $1,000 is the annual payment, r is the interest rate (in decimal form), and n is the number of payments (20).

We also need to account for the fact that Charlie wants to receive the first payment at the end of the 30th year, which means that the first payment is actually 30 years in the future. We can adjust for this by multiplying the result by (1+r)^30:

PV = $1,000 * (1 - (1 + 0.1)^-20) / 0.1 * (1+0.1)^30
PV = $9,262.24

Therefore, Charlie needs to invest $9,262.24 today in order to have his retirement annuity. Rounded to the nearest $10, the answer is $540, which is choice C.

Question 17

What is the present value of $250 received at the beginning of each year for 21 years? Assume that the first payment is received today.Use a discount rate of 12%,and round your answer to the nearest $10.

Accepted Answer

This is a case of annuity due as the first payment is received today. Using the formula for the present value of an annuity due, we have:

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

Where PV is the present value, A is the payment amount, r is the discount rate, and n is the number of payments. Plugging in the given values, we get:

PV = 250 * [(1 - (1 / (1 + 0.12)^21)) / 0.12] * (1 + 0.12)
PV = 2,116.693...

Rounding to the nearest $10, we get the answer of $2,117. Therefore, the best choice is C.

Question 18

A commercial bank will loan you $7,500 for two years to buy a car.The loan must be repaid in 24 equal monthly payments.The annual interest rate on the loan is 12% of the unpaid balance.What is the amount of the monthly payments?

Accepted Answer

The answer of A commercial bank will loan you $7,500...

Question 19

Your company has received a $50,000 loan from an industrial finance company.The annual payments are $6,202.70.If the company is paying 9% interest per year,how many loan payments must the company make?

Accepted Answer

The number of loan payments can be found using the formula for the present value of an annuity: $PV = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)$, where PV is the present value (loan amount), PMT is the annual payment, r is the annual interest rate, and n is the number of payments. Rearranging the formula to solve for n gives: $n = \frac{\log(1 - \frac{PV \times r}{PMT})}{\log(1 + r)}$. Substituting the given values ($PV = 50,000$, $PMT = 6,202.70$, $r = 0.09$) into the formula and solving for n yields approximately 15 payments.

Question 20

What is the present value of an annuity of $27 received at the beginning of each year for the next six years? The first payment will be received today,and the discount rate is 10% (round to nearest $10).

Accepted Answer

Using the formula for the present value of an annuity:
PV = A*((1 - (1+r)^(-n))/r)
PV = 27*((1 - (1+0.1)^(-6))/0.1)
PV = $130.39, rounded to nearest $10 is $130. Therefore, option B is the best choice.

Quiz 6: The Time Value of Money-Annuities and Other Topics