Question : The amount of Rs. 10,000 after 2 years, compounded annually with the rate of interest being 10% per annum during the first year and 12% per annum during the second year, would be (in rupees):
Option 1: 11,320
Option 2: 12,000
Option 3: 12,320
Option 4: 12,500
Correct Answer: 12,320
Solution :
Present value (P) = Rs. 10,000
Interest rate for 1st year,
$r_1$ = 10% per annum
Interest rate for 2nd year,
$r_2$ = 12% per annum
Time = 2 years
Amount(A) = P × (1 + $\frac{r_1}{100}$) × (1 + $\frac{r_2}{100}$)
= 10000 × (1 + $\frac{10}{100}$) × (1 + $\frac{12}{100}$)
= 10000 × ($\frac{110}{100}$) × ($\frac{112}{100}$)
= 110 × 112
= Rs. 12,320
Hence, the correct answer is 12,320.
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