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.
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