Question

On what sum will the compound interest at 5% per annum for two years compounded anually be 1640

Answer 1

1640=Principal[(1.05)²-1]
principal=16000

Answer 2

Given:

• Compound interest on a sum, C.I. = 1640

• Rate of interest per annum, R = 5 %

• Time for interest, t = 2 yrs

To find:

• Principal money, P =?

Formula required:

Formula to calculate Compound interest (C.I.) on a principal sum (P), at a rate of interest (R% ) for a time (t).

$\implies \boxed{\rm{C.I.=P{\bigg(1+\dfrac{R}{100}\bigg)}^t-P}}$

Solution:

Using formula for Compound interest

$\implies\rm{C.I.=P{\bigg(1+\dfrac{R}{100}\bigg)}^2-P}$

$\implies\rm{1640=P{\bigg(1+\dfrac{5}{100}\bigg)}^2-P}$

$\implies\rm{1640=P\bigg(1+\dfrac{25}{10000}+\dfrac{10}{100}\bigg)-P}$

$\implies\rm{1640=P\bigg(\dfrac{25}{10000}+\dfrac{10}{100}\bigg)}$

$\implies\rm{1640=P\bigg(\dfrac{25+1000}{10000}\bigg)}$

$\implies\rm{1640=P\bigg(\dfrac{1025}{10000}\bigg)}$

$\implies\rm{P=1640 \times \dfrac{10000}{1025}}$

$\implies \boxed{\boxed{\rm{P=16000}}}$