Question

Find the interest rate (or rates of return) in each of the following situations. Do not round intermediate calculations. Round your answers to the nearest whole number.

1. You borrow $650 and promise to pay back $676 at the end of 1 year.

     %

2. You lend $650 and receive a promise to be paid $676 at the end of 1 year.

     %

3. You borrow $60,000 and promise to pay back $289,075 at the end of 12 years.

     %

4. You borrow $16,000 and promise to make payments of $5,001.00 at the end of each of the next 5 years.

     %

Answer 1

Let Future Value = FV

Present Value = PV

Number of Years = n

Interest Rate = r

=> FV = PV(1+r)ⁿ

=> r = (FV/PV)^1/n - 1

(a) PV = 650

FV = 676

n = 1

=> r = (676/650)^1/1 - 1 = 0.04 or 4%

(b) PV = 650

FV = 676

n = 1

=> r = (676/650)^1/1 - 1 = 0.04 or 4%

(c) PV = 60000

FV = 289075

n = 12

=> r = (289075/60000)^1/12 - 1 = 0.14 or 14%

(d) PV = 16000

Payment received at end of each year = P = 5001

n = 5

=> PV = P/(1+r) + P/(1+r)² + ..... P/(1+r)ⁿ = P[1- (1+r)^-n]/r

=> 15000 = 5001[1- (1+r)^-5]/r

=> r = 20%