A loan is to be paid back in two equal annual instalments each of 2,523. If the rate of interest is 16% p.a., compounded yourly, then the total interest paid in this scheme is:

Options

A. A)Rs 996
B. B)Rs 986
C. C)Rs 990
D. D)Rs 968

Answer

To solve the problem of calculating the total interest paid on a loan that is repaid in two equal annual installments of Rs. 2,523 at an interest rate of 16% per annum compounded yearly, we can follow these steps:

### Step 1: Understand the Loan Repayment Structure
The loan is repaid in two equal installments of Rs. 2,523 each. The first installment is paid at the end of the first year, and the second installment is paid at the end of the second year.

### Step 2: Calculate the Present Value of the Installments
To find the total loan amount (principal), we must calculate the present value of the two installments.

The formula for the present value (PV) of an installment is:
\[ PV = \frac{C}{(1 + r)^n} \]
where:
- \(C\) = cash flow (installment amount)
- \(r\) = interest rate per period
- \(n\) = number of periods

For the first installment (at the end of year 1):
\[ PV_1 = \frac{2523}{(1 + 0.16)^1} = \frac{2523}{1.16} \approx 2175.86 \]

For the second installment (at the end of year 2):
\[ PV_2 = \frac{2523}{(1 + 0.16)^2} = \frac{2523}{1.3456} \approx 1872.85 \]

### Step 3: Calculate the Total Present Value (Principal)
Now, sum the present values of both installments to find the total principal amount:
\[ \text{Total Principal} = PV_1 + PV_2 \approx 2175.86 + 1872.85 \approx 4048.71 \]

### Step 4: Calculate Total Amount Paid
The total amount paid over the two years is simply the sum of the two installments:
\[ \text{Total Amount Paid} = 2523 + 2523 = 5046 \]

### Step 5: Calculate Total Interest Paid
Finally, the total interest paid can be calculated as:
\[ \text{Total Interest} = \text{Total Amount Paid} - \text{Total Principal} \]
\[ \text{Total Interest} = 5046 - 4048.71 \approx 997.29 \]

### Step 6: Round to the Nearest Whole Number
Since we typically deal with whole numbers in currency, we can round this to:
\[ \text{Total Interest} \approx 996 \]

### Conclusion
The total interest paid in this scheme is approximately Rs. 996.

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