Question

A woman borrows #75 000 at 8% per annum compound interest. At the end of the first year she pays back #31 000. At the end of the second year she repays 30 000. At the end of the third year she clears her debt completely. What is her final payment?​

Answer 1

The final payment is $75,009.12.

Step-by-step explanation:

To find the final payment, we need to calculate the total amount borrowed and the compound interest accrued over the three years.

First, let's calculate the total amount borrowed:

1. At the end of the first year, she has paid back $31,000.
2. At the end of the second year, she has paid back $30,000.
3. At the end of the third year, she has cleared her debt completely.

So, the total amount borrowed is $31,000 + $30,000 = $61,000.

Now, let's calculate the compound interest:

1. Use the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the interest rate, n is the number of times compounded per year, and t is the number of years.
2. Plug in the values: P = $61,000, r = 8%, n = 1 (annual compounding), and t = 3 years.
3. Calculate: A = $61,000(1 + 0.08/1)^(1*3) = $61,000(1.08)^3 = $75,009.12.

The final payment is $75,009.12.