it costs $24,893.75 to repay a loan of 17,500 at 6.5% annual interest. How many years does it take to repay the loan? I saw somebody asked this question, but the answer wasn't specific.

11.5 years

Step-by-step explanation:

The formula for the monthly payment of a loan is:

where

A = monthly payment

r = interest rate per period

n = number of periods

Assuming a monthly payment, we have

P = 17500

r = 0.065/12

The total amount of payments is the monthly payment times the number of payments, so

An = 24893.75

We can try 10 years. n = 10 * 12 = 120

An = 198.71 * 120 = 23845.08

The total amount of payments is too low.

Let's try 11 years.

n = 11 * 12 = 132

An = 185.92 * 132 = 24540.90

The total amount of payments is still too low.

Let's try 12 years.

n = 12 * 12 = 144

An = 185.92 * 144 = 25248.41

The total amount of payments is too high.

11 years is too little, and 12 years is too much.

Let's try 11.5 years.

n = 11.5 * 12 = 138

An = 180.39 * 138 = 24893.20

11.5 gives a total of payments of $24,893.20 which is very close to $23.893.75.

11.5 years

The total amount of payments is too high.