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.