Question

Rs. 7000 divided unequally and invested in scheme A (offered C.I. at 10% p.a. compounded annually) and in scheme B (offered S.I. at 15% p.a.) for 2 years and 3 years. If the investment earned from scheme A is 84% that earned from scheme B. Find the sum invested in scheme A?

Answer 1

Step-by-step explanation:

Let the amount invested at A be x and that invested at B be 7000 - x.

Compound interest accumulation formula is :

A = P(1 + I)ⁿ

A = accumulated amount

P = Principle amount

i = interest rate.

n = Period in years

Simple interest = Principle × rate × time

Amount = Principle + (Principle × rate × Time)

Doing the substitution we have :

Scheme A:

A = x(1.1)²

Scheme B :

A = (7000 - x) + (7000 - x) × 3 × 15/100

= 7000 - x + 3150 - 0.45x

= 10150 - 1.45x

From the question :

x(1.1)² = 84/100 × (10150 - 1.45x)

1.21x = 8526 - 1.218x

1.21x + 1.218x = 8526

2.428x = 8526

x = 8526/2.428

x = 3511.53

The amount invested in B = 7000 - 3511.53 = 3488.47

Amount in A : 3511.53

Amount in B : 3488.47