Question

How large must each annual payment before birr 100,000 loan to be repaid in equal installments at the end of each of the next 5 years? The interest rate is 10% compounded annually.

Answer 1

To determine the annual payment required to repay a loan of 100,000 birr over 5 years at an interest rate of 10% compounded annually, we can use the formula for the annuity payment, which is as follows:

\[
PMT = \frac{P \times r}{1 - (1 + r)^{-n}}
\]

Where:
- \( PMT \) is the annual payment
- \( P \) is the principal (loan amount)
- \( r \) is the annual interest rate (as a decimal)
- \( n \) is the number of years

In this case:
- \( P = 100,000 \) birr
- \( r = 0.10 \)
- \( n = 5 \)

Now we can substitute the values into the formula:

\[
PMT = \frac{100,000 \times 0.10}{1 - (1 + 0.10)^{-5}}
\]

First, calculate \( (1 + 0.10)^{-5} \):

\[
(1 + 0.10)^{-5} = (1.10)^{-5} \approx 0.620921
\]

Now, substitute this value into the formula:

\[
PMT = \frac{100,000 \times 0.10}{1 - 0.620921}
\]

Calculate \( 1 - 0.620921 \):

\[
1 - 0.620921 \approx 0.379079
\]

Now, substitute this value into the formula:

\[
PMT = \frac{100,000 \times 0.10}{0.379079} \approx \frac{10,000}{0.379079} \approx 26,391.27
\]

Thus, the annual payment required to repay the loan of 100,000 birr over 5 years at an interest rate of 10% compounded annually is approximately **26,391.27 birr**.