Question

What principal will give an amount of ₹ 27783 at an interest of 10 % compounded half-yearly for 1 year and 6 months?

Answer 1

The compound interest accumulation formula is :

P(1 + i)ⁿ = Accumulated amount

P = deposited amount (principle)

i = effective rate of interest = 10%

n = the number of years

Accumulated amount = 27783

CALCULATIONS :

Let p be the principle.

Since it is compounded semiannually the time is multiplied by two and the interest rate divided by two.

Hence :

i = 10/2 = 5%

n = 1.5 × 2 = 3

A = 27783

Doing the substitution :

P(1.05)³ = 27783

1.157625p = 27783

P = 27783/1.157625

P = 24000

Rs 24000