Question

A certain sum of money amounts to rs.550 in 3 years and to rs. 650 in 4 years. find the sum and rate of interest.

Answer 1

Accumulated amount formulae :

P(1 + i) ⁿ

P = principle amount

i = rate of interest

n = Time in years

Let the principle amount be pthenphenomenal :

Accumulated amount in 3 years

P(1 + i) ³ = 550

P = 550/(1 + i) ³

Accumulated amount in 4 years

P(1 + i) ⁴ = 650

P = 650/(1 + i) ⁴

Equating the two :

650/(1 + i) ⁴ = 550/(1 + i) ³

650 / 550 = (1 + i) ⁴ / (1 + i) ³

1.18181 = 1 + i

i = 1.18181 - 1 = 0.18181

= 0.18181 × 100 = 18.181%