A sum of money is borrowed and paid back in two annual installments of Tk. 882 each allowing 5% compound interest. The sum borrowed was :
Let's denote the principal amount (the sum borrowed) as "P" in Tk.
Given:
- The amount is paid back in two annual installments of Tk. 882 each.
- The interest is compounded annually at a rate of 5%.
Let's break down the repayment process:
First Installment:
- After the first year, the borrower pays Tk. 882.
- This payment includes both the principal and the interest accrued in the first year.
Second Installment:
- After the second year, the borrower pays another Tk. 882.
- Again, this payment includes both the principal and the interest accrued in the second year.
We can set up equations to represent these two installments:
After the first year: P + 5% of P = P + 0.05P = 1.05P So, after the first year, the remaining amount is 1.05P - 882.
After the second year: (1.05P - 882) + 5% of (1.05P - 882) = (1.05P - 882) + 0.05(1.05P - 882) = 1.1025P - 926.1 So, after the second year, the remaining amount is 1.1025P - 926.1 - 882.
Now, we know that after the second installment, the remaining amount should be zero because the loan is fully paid off. Therefore:
1.1025P - 926.1 - 882 = 0
Now, we can solve this equation to find the principal amount (P):
1.1025P - 1808.1 = 0
1.1025P = 1808.1
P = 1808.1 / 1.1025
P ≈ 1640
So, the principal amount borrowed was approximately Tk. 1640.
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