Loan Amortization
1. **Stating the problem:**
Mr. Afian borrows Tk. 60000 at 12% annual interest and wants to repay the loan in 20 equal annual installments starting at the end of the first year. We need to find the amount of each annual payment.
2. **Understanding the problem:**
This is a loan amortization problem where the loan amount $P=60000$ is repaid with equal annual payments $A$ over $n=20$ years at an interest rate $i=0.12$ (12%).
3. **Formula for the annual payment:**
The formula for the installment payment $A$ for a loan is:
$$
A = P \times \frac{i(1+i)^n}{(1+i)^n - 1}
$$
4. **Plugging in the values:**
$$
A = 60000 \times \frac{0.12(1+0.12)^{20}}{(1+0.12)^{20} - 1}
$$
5. **Calculating $(1+0.12)^{20}$:**
$$
(1.12)^{20} \approx 9.6463
$$
6. **Substitute back:**
$$
A = 60000 \times \frac{0.12 \times 9.6463}{9.6463 - 1} = 60000 \times \frac{1.1576}{8.6463}
$$
7. **Calculate the fraction:**
$$
\frac{1.1576}{8.6463} \approx 0.1338
$$
8. **Calculate the annual payment $A$:**
$$
A = 60000 \times 0.1338 = 8028
$$
9. **Final answer:**
The annual payment necessary to repay the loan is approximately Tk. 8028.
(This differs from the example final amount Tk. 336,389 which likely includes total payments over 20 years, not the single annual payment.)