1a. An investment offers an annual return of 14%. What is the effective annual r

Question

1a.

An investment offers an annual return of 14%. What is the effective annual rate of this investment if interest is compounded:
(a) Annually
(b) Monthly
(c) Daily
(Round your answers to 4 decimal places. (e.g., 32.1615))

1b. Shippon Co. signed a contract that will entitle them to $9,000 every six months for the next ten years. They want their money now. A bank has agreed to buy the contract with a discount rate of 7%, compounded semiannually. How much will the bank be willing to pay Shippon currently if Shippon assigns its rights to receive payments under the contract to the bank? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 5,432.16))

An investment offers an annual return of 14%. What is the effective annual rate of this investment if interest is compounded:
(a) Annually
(b) Monthly
(c) Daily
(Round your answers to 4 decimal places. (e.g., 32.1615))

1b. Shippon Co. signed a contract that will entitle them to $9,000 every six months for the next ten years. They want their money now. A bank has agreed to buy the contract with a discount rate of 7%, compounded semiannually. How much will the bank be willing to pay Shippon currently if Shippon assigns its rights to receive payments under the contract to the bank? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 5,432.16))

Explanation / Answer

Answer 1a.

EAR = (1 + APR/n)^n - 1, where n is number of compounding per year

If interest is compounded annually:

Annual Interest Rate = 14%

EAR = 14%

If interest is compounded monthly:

Annual Interest Rate = 14%

EAR = (1 + 0.14/12)^12 - 1
EAR = 1.01167^12 - 1
EAR = 1.1494 - 1
EAR = 0.1494 or 14.94%

If interest is compounded daily:

Annual Interest Rate = 14%

EAR = (1 + 0.14/365)^365 - 1
EAR = 1.000384^365 - 1
EAR = 1.1504 - 1
EAR = 0.1504 or 15.04%

Answer 1b.

Semiannual Payment = $9,000
Semiannual Period = 20 (10 years)
Annual Interest Rate = 7%
Semiannual Interest Rate = 3.5%

Present Value = $9,000 * PVIFA(3.5%, 20)
Present Value = $9,000 * (1 - (1/1.035)^20) / 0.035
Present Value = $9,000 * 14.21240
Present Value = $127,911.60

So, bank will pay $127,911.60 to Shippon Co.

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