Shubhaiaxmi took a loan of Rs 18000 from Surya Finance to purchase a TV set. If the company charges compound interest at 12% per annum during the first year and `12(1)/(2)%` per annum during the second year, how much will she have to pay after 2 years?

Answer

To solve the problem step by step, we will calculate the total amount Shubhaiaxmi has to pay after 2 years, considering the compound interest rates for each year.

### Step 1: Identify the principal amount and interest rates
- Principal amount (P) = Rs 18,000
- Interest rate for the first year (R1) = 12% per annum
- Interest rate for the second year (R2) = 12.5% per annum (which is 12 1/2%)

### Step 2: Calculate the amount after the first year
Using the formula for compound interest:
\[ A = P \left(1 + \frac{R}{100}\right) \]
For the first year:
\[ A_1 = 18000 \left(1 + \frac{12}{100}\right) \]
\[ A_1 = 18000 \left(1 + 0.12\right) \]
\[ A_1 = 18000 \times 1.12 \]
\[ A_1 = 20160 \]

### Step 3: Calculate the amount after the second year
Now, we will use the amount from the first year as the principal for the second year:
\[ A_2 = A_1 \left(1 + \frac{R2}{100}\right) \]
\[ A_2 = 20160 \left(1 + \frac{12.5}{100}\right) \]
\[ A_2 = 20160 \left(1 + 0.125\right) \]
\[ A_2 = 20160 \times 1.125 \]
\[ A_2 = 22680 \]

### Step 4: Conclusion
The total amount Shubhaiaxmi has to pay after 2 years is Rs 22,680.

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