Question

Find the principal if the difference between C.I and S.l on it at 15% p.a for 3 years is ₹ 1134

Answer 1

Rate of interest (r) = 15% p.a

Time period (n) = 3 years

Difference between C.I and S.I is given as 1134

Principal = ? → required to find

Using formula for difference

Simple Interest S.I = `"Pnr"/100`

Compound Interest C.I = p(1 + i)ⁿ – p

C.I − S.I = `"P"[(1 + "i")^"n" - 1 - "nr"/100]`

1134 = `"P"[(1 + 15/100)^3 - 1 - (3 xx 15)/100]`

1134 = `"P"[(115/100)^3 - 1 - 45/100]`

1134 = P[(1.15)³ – 1 – 0.45]

= P(1.52 – 1.45)

= P(0.07)

∴ P = `(1134 xx 100)/(0.07 xx 100)`

= `113400/7`

P = ₹ 16200