A man borrows 12,500 at 20% compound interest. At the end of every year he pays 2000 as part repayment. How much does he still owe after three such instalments?

Options

A. 12000
B. 14320
C. 15600
D. None of these

Answer

To solve the problem step by step, let's break down the calculations for each year, considering the compound interest and the repayments made.

### Step 1: Calculate the amount owed after the first year.
- **Principal Amount (P)**: ₹12,500
- **Rate of Interest (R)**: 20%
- **Time (T)**: 1 year

The formula for compound interest is:
\[ A = P(1 + r)^t \]
Where:
- \( A \) is the amount after time \( t \)
- \( P \) is the principal amount
- \( r \) is the rate of interest (in decimal)
- \( t \) is the time in years

First, convert the percentage to decimal:
\[ r = \frac{20}{100} = 0.20 \]

Now, calculate the amount after the first year:
\[ A = 12500(1 + 0.20)^1 \]
\[ A = 12500(1.20) \]
\[ A = 15000 \]

Now, subtract the repayment of ₹2000:
\[ \text{Amount after repayment} = 15000 - 2000 = 13000 \]

### Step 2: Calculate the amount owed after the second year.
Now, take the amount after the first year as the principal for the second year.
- **New Principal Amount (P)**: ₹13,000

Calculate the amount after the second year:
\[ A = 13000(1 + 0.20)^1 \]
\[ A = 13000(1.20) \]
\[ A = 15600 \]

Subtract the repayment of ₹2000:
\[ \text{Amount after repayment} = 15600 - 2000 = 13600 \]

### Step 3: Calculate the amount owed after the third year.
Now, take the amount after the second year as the principal for the third year.
- **New Principal Amount (P)**: ₹13,600

Calculate the amount after the third year:
\[ A = 13600(1 + 0.20)^1 \]
\[ A = 13600(1.20) \]
\[ A = 16320 \]

Subtract the repayment of ₹2000:
\[ \text{Amount after repayment} = 16320 - 2000 = 14320 \]

### Final Amount Owed
After three years of repayments, the amount still owed is **₹14,320**.

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