Question

If you borrow $9,000 and agree to repay the loan in six equal annual payments
al an interest rate of 10%, what will the annual payment be? What if you make
the first payment on the loan at the end of second year?

Answer 1

Borrowed money = $9,000

Time = 6 years (every payment at end of the year)

Rate of interest = 10%

Assume Installment amount = $X

After one year of borrow money till the first installment is paid, it gets rate of interest for one year which makes the payment = $9,000 * 1.1 = $9,900. After installment, payment left is $9,000 - X

In whole 2nd year, this would get rate of interest which makes it ($9,000 - X) * 1.1 while payment after 2nd year makes it (($9,000 - X) * 1.1 ) - X

Here, we gets a pattern that in each year we multiply the equation by 1.1 and subtract X from it.

Till six years, the pattern would be:

((((((((((($9,900 - X) * 1.1 ) - X ) * 1.1) - X) * 1.1) - X) * 1.1) - X) * 1.1) - X) = 0

9900 = 4.79X

X = 2066.80

Thus every installment would be equal to $2066.8.

If the first payment is made after end of second year, the pattern would become:

(((((((((((((9000 * 1.1 * 1.1) - X) * 1.1 ) - X) * 1.1) - X) * 1.1) - X) * 1.1) - X) * 1.1) - X) = 0

X = $2,273.48