Find the interest rates earned on each of the following Roun

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

You borrow $660 and promise to pay back $726 at the end of 1 year

You lend $660 and the borrower promises to pay you $726 at the end of 1 year.

You borrow $57,000 and promise to pay back $415,393 at the end of 12 years.

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

Solution

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

1.

726=660(1+r/100)^1

(726/660)^1=(1+r/100)

(1+r/100)=1.1

r=(1.1-1)*100

=10%

2.

726=660(1+r/100)^1

(726/660)^1=(1+r/100)

(1+r/100)=1.1

r=(1.1-1)*100

=10%

3.

415393=57000(1+r/100)^12

(415393/57000)^(1/12)=(1+r/100)

(1+r/100)=1.18

r=(1.18-1)*100

=18%

4.

Let 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%(Approx).