A sum of money was borrowed and paid back in two equal annual instalments of ₹980, allowing 4% compound interest. The sum (in ₹, to the nearest tens) borrowed was:

Question

Question

This question was previously asked in

SSC CGL 2021 Tier-I (Held On : 11 April 2022 Shift 3)

Answer 1

Given:

Each installment = ₹ 980

Rate of interest = 4%

Number of years = 2

Formula used:

In case of compound interest, borrowed money = x/(1 + r/100) + x/(1 + r/100)² + ..... + x/(1 + r/100)ⁿ

Calculation:

The borrowed money = \(\frac{980}{(1+\frac{4}{100})}+\frac{980}{(1+\frac{4}{100})^{2}}\)

= \(\frac{980}{\frac{26}{25}}+\frac{980}{\frac{26}{25}×\frac{26}{25}}\)

= [980 × (25/26)] + [980 × (25/26) × (25/26)]

= 980 [(25/26) + (25/26) × (25/26)]

= \(980 \left[\frac{(25×26)+(25×25)}{26×26} \right]\)

= 980 × [(650 + 625)/676]

= 980 × (1275/676)

= 1848.372...

≈ 1850 (in ₹, to the nearest tens)

∴ The sum (in ₹, to the nearest tens) borrowed was ₹ 1850