Question

On what sum will the compound interest at 5% per annum for two years compounded annually be 1,640?​

Answer 1

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).

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

Solution:

Using formula for Compound interest

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

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

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

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

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

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

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

$\implies\underline{\underline{\boxed{\sf{P=16000}}}}\;\;\purple{\bigstar}$

Therefore,

• Principal sum is equal to 16000.