Arun took a loan of Rs 390625 from Kuber Finance. If the company charges interest at 16% per annum, compounded quarterly, what amount will discharge his debt after one year?

Answer

To solve the problem of how much Arun will need to pay back after one year on a loan of Rs 390625 with an interest rate of 16% per annum compounded quarterly, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs 390625
- Rate of interest (R) = 16% per annum
- Time (T) = 1 year
- Compounding frequency (n) = 4 (since it is compounded quarterly)

### Step 2: Convert the annual interest rate to a quarterly rate
To find the quarterly interest rate, we divide the annual rate by the number of compounding periods in a year:
\[ \text{Quarterly Rate} = \frac{R}{n} = \frac{16\%}{4} = 4\% \]
Convert this percentage to a decimal for calculations:
\[ \text{Quarterly Rate} = \frac{4}{100} = 0.04 \]

### Step 3: Calculate the total amount using the compound interest formula
The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{n}\right)^{nT} \]
Substituting the known values into the formula:
\[ A = 390625 \left(1 + 0.04\right)^{4 \times 1} \]
\[ A = 390625 \left(1.04\right)^{4} \]

### Step 4: Calculate \( (1.04)^4 \)
Now we need to calculate \( (1.04)^4 \):
\[ (1.04)^4 = 1.16985856 \quad (\text{approximately}) \]

### Step 5: Calculate the total amount \( A \)
Now substitute back into the formula:
\[ A = 390625 \times 1.16985856 \approx 457663.25 \]

### Final Result
Thus, the amount that Arun will need to pay back after one year is approximately Rs 457663.25.

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