Question

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

A. You borrow $750 and promise to pay back $795 at the end of 1 year.

B. You lend $750 and the borrower promises to pay you $795 at the end of 1 year.

C. You borrow $80,000 and promise to pay back $186,532 at the end of 11 years.

D. You borrow $9,000 and promise to make payments of $2,684.80 at the end of each year for 5 years.

Answer 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.

a.

795=750(1+r/100)^1

(795/750)=(1+r/100)

(1+r/100)=1.06

Hence r=(1.06-1)*100

=6%

b.

795=750(1+r/100)^1

(795/750)=(1+r/100)

(1+r/100)=1.06

Hence r=(1.06-1)*100

=6%

c.

186532=80000(1+r/100)^11

(186532/80000)^(1/11)=(1+r/100)

(1+r/100)=1.08

Hence r=(1.08-1)*100

=8%

d.

Let interest rate be x%

At this interest rate;present value of inflows=$9000

9000=2684.8/1.0x+2684.8/1.0x^2+2684.8/1.0x^3+2684.8/1.0x^4+2684.8/1.0x^5

(9000/2684.8)=1/1.0x+1/1.0x^2+........+1/1.0x^5

1/1.0x+1/1.0x^2+........+1/1.0x^5=3.3522

Hence interest rate=15%(Also looking at present value of annuity factor(15%,5 years).