Anita borrowed two equal sums at the beginning of two successive years at 10% compound interest. At the end of the second year, she paid Rs. 12,474 to settle her debts. How much did she borrow each year?
1. Rs. 4,800
2. Rs. 5,000
3. Rs. 5,400
4. Rs. 5,600
1. Rs. 4,800
2. Rs. 5,000
3. Rs. 5,400
4. Rs. 5,600
Correct Answer – Option 3 : Rs. 5,400
Given:
Rate of interest = 10%
At the end of second year, money paid by her = Rs. 12474
Concept used:
A = P × (1 + R/100)T
Where,
A → Amount
P → Principal
R → Rate of interest
T → Time
Calculations:
Let the principal be 100x
Money after completion of first year = 100x × (1 + 10/100)1
⇒ 100x × 110/100 = 110x
She borrowed the same principal in second year
So principal for second year = 110x + 100x = 210x
Money after completion of second year = 210x × (1 + 10/100)1
⇒ 231x = 12474
⇒ x = 54
Money borrowed each year =100x = 5400
∴ Money borrowed each year is Rs. 5400