Question 1

What is the PV of an annuity due with 5 payments of $2,500 at an interest rate of 5.5%?
A) $11,262.88
B) $11,826.02
C) $12,417.32
D) $13,038.19
E) $13,690.10

Accepted Answer

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Question 2

Your father is considering purchasing an annuity that pays $5,000 at the beginning of each year for 5 years.He could earn 4.5% on his money in other investments with equal risk.What is the most he should pay for the annuity?
A) 20,701
B) $21,791
C) $22,938
D) $24,085
E) $25,289

Accepted Answer

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Question 3

After receiving a reward for information leading to the arrest of a notorious criminal, you are considering investing it in an annuity that pays $5,000 at the end of each year for 20 years.You could earn 5% on your money in other investments with equal risk.What is the most you should pay for the annuity?
A) $50,753
B) $53,424
C) $56,236
D) $59,195
E) $62,311

Accepted Answer

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Question 4

Suppose People's bank offers to lend you $10,000 for 1 year on a loan contract that calls for you to make interest payments of $250.00 at the end of each quarter and then pay off the principal amount at the end of the year.What is the effective annual rate on the loan?
A) 8.46%
B) 8.90%
C) 9.37%
D) 9.86%
E) 10.38%

Accepted Answer

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Question 5

All other things held constant, the present value of a given annual annuity increases as the number of periods per year increases.

Accepted Answer

The present value of an annuity is inversely related to the interest rate (discount rate) used in the calculation; it is not directly affected by the number of periods per year for the annuity payments. Increasing the number of periods per year typically involves adjusting the interest rate for each period, which could affect the present value, but the statement as given does not hold true as a general principle.

Question 6

You are considering two equally risky annuities, each of which pays $15,000 per year for 20 years.Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due.Which of the following statements is CORRECT?
A) If the going rate of interest decreases from 10% to 0%, the difference between the present value of ORD and the present value of DUE would remain constant.
B) The present value of ORD must exceed the present value of DUE, but the future value of ORD may be less than the future value of DUE.
C) The present value of DUE exceeds the present value of ORD, while the future value of DUE is less than the future value of ORD.
D) The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the future value of DUE.
E) The present value of DUE exceeds the present value of ORD, and the future value of DUE also exceeds the future value of ORD.

Accepted Answer

The present value of an annuity due is higher than that of an ordinary annuity because payments are received at the beginning of each period, allowing each payment to accrue interest for an additional period. Similarly, the future value of an annuity due is higher because each payment is invested for an additional period.

Question 7

Because your mother is about to retire, she wants to buy an annuity that will provide her with $75,000 of income a year for 20 years, with the first payment coming immediately.The going rate on such annuities is 5.25%.How much would it cost her to buy the annuity today?
A) $825,835
B) $869,300
C) $915,052
D) $963,213
E) $1,011,374

Accepted Answer

We can use the present value of an annuity formula to calculate the cost of the annuity:
PV = PMT * ((1 - (1 + r)^-n) / r)
where PV is the present value of the annuity, PMT is the annual payment, r is the interest rate, and n is the number of payments (in years).
Plugging in the given values, we get:
PV = $75,000 * ((1 - (1 + 0.0525)^-20) / 0.0525) = $963,212.57
Therefore, the cost to buy the annuity today would be $963,213, which is closest to option D.

Question 8

Pacific Bank pays a 4.50% nominal rate on deposits, with monthly compounding.What effective annual rate (EFF%) does the bank pay?
A) 3.72%
B) 4.13%
C) 4.59%
D) 5.05%
E) 5.56%

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Question 9

Suppose your credit card issuer states that it charges a 15.00% nominal annual rate, but you must make monthly payments, which amounts to monthly compounding.What is the effective annual rate?
A) 15.27%
B) 16.08%
C) 16.88%
D) 17.72%
E) 18.61%

Accepted Answer

The effective annual rate (EAR) can be calculated using the formula: EAR = (1 + i/n)ⁿ - 1, where i is the nominal annual interest rate and n is the number of compounding periods per year. In this case, i = 15.00% or 0.15, and n = 12 (monthly compounding). Plugging these values into the formula gives EAR = (1 + 0.15/12)¹² - 1 ≈ 0.16075 or 16.08%.

Question 10

You just deposited $2,500 in a bank account that pays a 4.0% nominal interest rate, compounded quarterly.If you also add another $5,000 to the account one year (4 quarters) from now and another $7,500 to the account two years (8 quarters) from now, how much will be in the account three years (12 quarters) from now?
A) $15,234.08
B) $16,035.88
C) $16,837.67
D) $17,679.55
E) $18,563.53

Accepted Answer

To find the total amount in the account three years from now, we need to calculate the future value of each deposit separately, considering the compound interest formula: $A = P(1 + \frac{r}{n})^{nt}$, where:- $A$ is the amount of money accumulated after n years, including interest.- $P$ is the principal amount (the initial amount of money).- $r$ is the annual interest rate (decimal).- $n$ is the number of times that interest is compounded per year.- $t$ is the time the money is invested for in years.1. For the initial $2,500 deposited, it will compound for 3 years (12 quarters):$$A_1 = 2500(1 + \frac{0.04}{4})^{4*3} = 2500(1 + 0.01)^{12} = 2500(1.01)^{12}$$2. For the $5,000 added after 1 year, it will compound for 2 years (8 quarters):$$A_2 = 5000(1 + \frac{0.04}{4})^{4*2} = 5000(1 + 0.01)^{8} = 5000(1.01)^{8}$$3. For the $7,500 added after 2 years, it will compound for 1 year (4 quarters):$$A_3 = 7500(1 + \frac{0.04}{4})^{4*1} = 7500(1 + 0.01)^{4} = 7500(1.01)^{4}$$Calculating each:- $A_1 = 2500(1.01)^{12} ≈ 2816.89$- $A_2 = 5000(1.01)^{8} ≈ 5418.99$- $A_3 = 7500(1.01)^{4} ≈ 7800$Adding them together:$$Total = A_1 + A_2 + A_3 ≈ 2816.89 + 5418.99 + 7800 ≈ 16035.88$$Therefore, the total amount in the account three years from now will be approximately $16,035.88.

Question 11

Suppose United Bank offers to lend you $10,000 for one year at a nominal annual rate of 8.00%, but you must make interest payments at the end of each quarter and then pay off the $10,000 principal amount at the end of the year.What is the effective annual rate on the loan?
A) 8.24%
B) 8.45%
C) 8.66%
D) 8.88%
E) 9.10%

Accepted Answer

The effective annual rate (EAR) can be calculated using the formula for compound interest when interest is compounded quarterly. The nominal annual rate is 8.00%, and since interest is paid quarterly, the quarterly interest rate is 8.00%/4 = 2.00%. The formula for EAR when interest is compounded quarterly is (1 + (nominal rate / number of compounding periods))^number of compounding periods - 1. Plugging in the values, we get (1 + 0.08/4)^(4) - 1 = (1 + 0.02)^(4) - 1 = 1.08243216 - 1 = 0.0824 or 8.24%.

Question 12

What is the PV of an ordinary annuity with 10 payments of $2,700 if the appropriate interest rate is 5.5%?
A) $16,576
B) $17,449
C) $18,367
D) $19,334
E) $20,352

Accepted Answer

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Question 13

A new investment opportunity for you is an annuity that pays $550 at the beginning of each year for 3 years.You could earn 5.5% on your money in other investments with equal risk.What is the most you should pay for the annuity?
A) $1,412.84
B) $1,487.20
C) $1,565.48
D) $1,643.75
E) $1,725.94

Accepted Answer

To find the most you should pay for the annuity, we need to calculate the present value of the annuity using the formula:

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

Where PV is the present value, PMT is the payment amount, r is the interest rate, and n is the number of periods.

In this case, PMT = $550, r = 5.5% = 0.055, and n = 3.

Plugging in these values, we get:

PV = $550 x ((1 - (1 / (1 + 0.055)^3)) / 0.055)
PV = $1,565.48

Therefore, the most you should pay for the annuity is $1,565.48. Choice C is the closest to this amount.

Question 14

What is the PV of an ordinary annuity with 5 payments of $4,700 if the appropriate interest rate is 4.5%?
A) $16,806
B) $17,690
C) $18,621
D) $19,601
E) $20,633

Accepted Answer

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Question 15

An uncle of yours who is about to retire wants to sell some of his stock and buy an annuity that will provide him with income of $50,000 per year for 30 years, beginning a year from today.The going rate on such annuities is 7.25%.How much would it cost him to buy such an annuity today?
A) $574,924
B) $605,183
C) $635,442
D) $667,214
E) $700,575

Accepted Answer

The cost of the annuity can be calculated using the present value formula for annuities: PV = PMT × [(1 - (1 + r)^-n) / r], where PMT is the annual payment ($50,000), r is the annual interest rate (7.25% or 0.0725), and n is the number of years (30). Plugging in these values gives: PV = $50,000 × [(1 - (1 + 0.0725)^-30) / 0.0725] = $605,183.

Question 16

You are considering two equally risky annuities, each of which pays $25,000 per year for 10 years.Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due.Which of the following statements is CORRECT?
A) If the going rate of interest decreases from 10% to 0%, the difference between the present value of ORD and the present value of DUE would remain constant.
B) A rational investor would be willing to pay more for DUE than for ORD, so their market prices should differ.
C) The present value of DUE exceeds the present value of ORD, while the future value of DUE is less than the future value of ORD.
D) The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the future value of DUE.
E) The present value of ORD exceeds the present value of DUE, while the future value of DUE exceeds the future value of ORD.

Accepted Answer

Investment DUE, due to the fact that it starts paying immediately, is more valuable than ORD which starts paying after one year. Therefore, a rational investor would be willing to pay more for DUE than for ORD, which results in their market prices being different. Option B states this fact correctly. The other options either contain errors or are not true statements.

Question 17

Partners Bank offers to lend you $50,000 at a nominal rate of 5.0%, simple interest, with interest paid quarterly.An offer to lend you the $50,000 also comes from Community Bank, but it will charge 6.0%, simple interest, with interest paid at the end of the year.What's the difference in the effective annual rates charged by the two banks?
A) 1.56%
B) 1.30%
C) 1.09%
D) 0.91%
E) 0.72%

Accepted Answer

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Question 18

A "growing annuity" is a cash flow stream that grows at a constant rate for a specified number of periods.

Accepted Answer

A growing annuity is a cash flow stream where the payments increase at a constant rate for a specified number of periods. This is in contrast to a regular annuity where the payments are fixed.

Question 19

Southwestern Bank offers to lend you $50,000 at a nominal rate of 6.5%, compounded monthly.The loan (principal plus interest) must be repaid at the end of the year.Woodburn Bank also offers to lend you the $50,000, but it will charge an annual rate of 7.0%, with no interest due until the end of the year.How much higher or lower is the effective annual rate charged by Woodburn versus the rate charged by Southwestern?
A) 0.52%
B) 0.44%
C) 0.36%
D) 0.30%
E) 0.24%

Accepted Answer

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Question 20

Your friend offers to pay you an annuity of $2,500 at the end of each year for 3 years in return for cash today.You could earn 5.5% on your money in other investments with equal risk.What is the most you should pay for the annuity?
A) $5,493.71
B) $5,782.85
C) $6,087.21
D) $6,407.59
E) $6,744.83

Accepted Answer

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Quiz 4: Time Value of Money

What is the PV of an annuity due with 5 payments of $2,500 at an interest rate of 5.5%?

Your father is considering purchasing an annuity that pays $5,000 at the beginning of each year for 5 years.He could earn 4.5% on his money in other investments with equal risk.What is the most he should pay for the annuity?

Suppose People's bank offers to lend you $10,000 for 1 year on a loan contract that calls for you to make interest payments of $250.00 at the end of each quarter and then pay off the principal amount at the end of the year.What is the effective annual rate on the loan?

All other things held constant, the present value of a given annual annuity increases as the number of periods per year increases.

You are considering two equally risky annuities, each of which pays $15,000 per year for 20 years.Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due.Which of the following statements is CORRECT?

Because your mother is about to retire, she wants to buy an annuity that will provide her with $75,000 of income a year for 20 years, with the first payment coming immediately.The going rate on such annuities is 5.25%.How much would it cost her to buy the annuity today?

Pacific Bank pays a 4.50% nominal rate on deposits, with monthly compounding.What effective annual rate (EFF%) does the bank pay?

Suppose your credit card issuer states that it charges a 15.00% nominal annual rate, but you must make monthly payments, which amounts to monthly compounding.What is the effective annual rate?

Suppose United Bank offers to lend you $10,000 for one year at a nominal annual rate of 8.00%, but you must make interest payments at the end of each quarter and then pay off the $10,000 principal amount at the end of the year.What is the effective annual rate on the loan?

What is the PV of an ordinary annuity with 10 payments of $2,700 if the appropriate interest rate is 5.5%?

A new investment opportunity for you is an annuity that pays $550 at the beginning of each year for 3 years.You could earn 5.5% on your money in other investments with equal risk.What is the most you should pay for the annuity?

What is the PV of an ordinary annuity with 5 payments of $4,700 if the appropriate interest rate is 4.5%?

An uncle of yours who is about to retire wants to sell some of his stock and buy an annuity that will provide him with income of $50,000 per year for 30 years, beginning a year from today.The going rate on such annuities is 7.25%.How much would it cost him to buy such an annuity today?

You are considering two equally risky annuities, each of which pays $25,000 per year for 10 years.Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due.Which of the following statements is CORRECT?

A "growing annuity" is a cash flow stream that grows at a constant rate for a specified number of periods.

Your friend offers to pay you an annuity of $2,500 at the end of each year for 3 years in return for cash today.You could earn 5.5% on your money in other investments with equal risk.What is the most you should pay for the annuity?