Question

a sum becomes 4800 after 2 years and 6400 after 4 years when compounded
annually. find the sum

Answer 1

The compound interest accumulation finction is given by :

A = p( 1 + i)ⁿ

A = the mount

P = the principle amount

i = the rate of interest

n = Time in years

Doing the substitution we have :

4800 = P (1 + i)²

P = 4800/(1 + i)²

6400 = P(1 + i)⁴

P = 6400/(1 + i)⁴

4800/(1 + i)² = 6400/(1 + i)⁴

Let (1 + i) = y

4800/y² = 6400/y⁴

4800/6400 = y²/y⁴

0.75 = 1/y²

0.75y² = 1

y² = 1/0.75 = 1.3333

y = 1.154

since y = 1 + i

1.154 = 1 + i

i = 1.154 - 1 = 0.154

We want P

Doing the substitution we have :

4800/(1.154)² = 3604.37

The sum is :

= 3604.37