Problem 5-12 Effective rate of interest Find the interest rates earned on each o

Question

Problem 5-12
Effective rate of interest

Find the interest rates earned on each of the following. Round each answer to two decimal places.

You borrow $750 and promise to pay back $780 at the end of 1 year.

%

You lend $750 and the borrower promises to pay you $780 at the end of 1 year.

%

You borrow $84,000 and promise to pay back $362,078 at the end of 14 years.

%

You borrow $14,000 and promise to make payments of $3,693.20 at the end of each year for 5 years.

%

Uneven cash flow stream

Find the present values of the following cash flow streams at an 11% discount rate. Round your answers to the nearest cent.

Stream A $  

Stream B $  

What are the PVs of the streams at a 0% discount rate?

Stream A $  

Stream B $  

Problem 5-10
Present and future values for different interest rates

Find the following values. Compounding/discounting occurs annually. Round your answers to the nearest cent.

a. An initial $500 compounded for 10 years at 7%.

$  

b. An initial $500 compounded for 10 years at 14%.

$  

c. The present value of $500 due in 10 year at 7%.

$  

d. The present value of $1,925 due in 10 years at 14%.

$  

e. The present value of $1,925 due in 10 years at 7%.

$  

Define present value.

-Select-

The present value is the value today of a sum of money to be received in the future and in general is less than the future value.

The present value is the value today of a sum of money to be received in the future and in general is greater than the future value.

The present value is the value today of a sum of money to be received in the future and in general is equal to the future value.

The present value is the value in the future of a sum of money to be received today and in general is less than the future value.

The present value is the value in the future of a sum of money to be received today and in general is greater than the future value.

How are present values affected by interest rates?

-Select-

Assuming positive interest rates, the present value will increase as the interest rate increases

.Assuming positive interest rates, the present value will decrease as the interest rate increases.

Assuming positive interest rates, the present value will decrease as the interest rate decreases.

Assuming positive interest rates, the present value will not change as the interest rate increases.

Assuming positive interest rates, the present value will not change as the interest rate decreases.

Explanation / Answer

1) Rate of return, r = (FV / PV)^(1/n) - 1 = (780 / 750)^(1/1) - 1 = 4%

2) Rate of return, r = (362,078 / 84,000)^(1/14) - 1 = 11.00%

3) Rate of return for annuity can be calculated using I/Y function on a calculator

N = 5, PMT = 3,693.2, PV = -14,000, FV = 0 => Compute I/Y = 10.00%

4) PV = CF1 / (1 + r) + CF2 / (1 + r)^2 + CF3 / (1 + r)^3 + CF4 / (1 + r)^4 + CF5 / (1 + r)^5

With r = 11%,

For A, CF1 = 100...CF5 = 250 => PV = $1,008.99

For B, CF1 = 250... CF5 = 100 => PV = $1,055.11

If r = 0%, then PV for both streams = sum of CF = 1,400

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