Anita borrowed two equal sums at the beginning of two successive years

1.	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. 4,8002. Rs. 5,0003. Rs. 5,4004. Rs. 5,600
Answer» 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

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. 4,8002. Rs. 5,0003. Rs. 5,4004. Rs. 5,600

Answer» 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

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