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.

a.You borrow $650 and promise to pay back $715 at the end of 1 year.

b.You lend $650 and the borrower promises to pay you $715 at the end of 1 year.

c.You borrow $91,000 and promise to pay back $354,534 at the end of 12 years.

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

Answer 1

1.We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

715=650(1+r/100)^1

(715/650)^1=(1+r/100)

(1+r/100)=1.1

Hence interest rate=(1.1-1)*100

=10%

2.

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

715=650(1+r/100)^1

(715/650)^1=(1+r/100)

(1+r/100)=1.1

Hence interest rate=(1.1-1)*100

=10%

3.

354534=91000(1+r/100)^12

(354534/91000)^(1/12)=1+r/100

1+r/100=1.12

r=(1.12-1)*100

=12%

4.

Let interest rate be x%

At this rate;present value of payments=$16000

16000=5001/1.0x+5001/1.0x^2+5001/1.0x^3+5001/1.0x^4+5001/1.0x^5

Hence x=interest rate=17%