Question

Shruti borrows Rs 12000 at 10% per annum for 3 years at simple interest and Shalini

borrows the same amount for the same period at 8% per annum compounded annually. Who

pays more interest and by how much?
​

Answer 1

amount that shruti pays is 15600 as simple interest on 12000 is 3600

whereas shalini pays 15972 as compound interest on 12000 is 3972

therefore shalini pays more interest

Answer 2

Given,

Amount Shruti borrowed = Rs. 12000,

Time = 3 years,

At rate = 10% per annum simple interest.

Shalini borrowed the same amount,

At rate = 8% per annum, compounded annually,

For time = 3 years.

To find,

Who pays more interest, and,

By how much.

Solution,

It can be found who pays more interest, by calculating the interest paid by both of them separately.

Interest paid by Shruti,

Since Shruti has borrowed at Simple interest (SI). So, interest on the principal (P) at (r)% rate per annum for (t) years will be given by the formula,

$SI=\frac{Prt}{100}$

Here,

P = Rs. 12000, r = 10%, and, t = 3 years

⇒ $SI = \frac{12000\times 10\times 3}{100}$

⇒ $SI =Rs.\hspace{3}3600$

Interest paid by Shalini,

Shalini has borrowed the same amount at compound interest. Now, compound interest on a principal (P) at (r)% rate per annum for (t) years compounded annually is given by,

$CI=P\{(1+\frac{r}{100} )^t-1\}$

Here,

P = Rs. 12000, r = 8%, and, t = 3 years

⇒ $CI=12000\{(1+\frac{8}{100} )^3-1\}$

⇒ $CI=12000\{(\frac{108}{100} )^3-1\}$

⇒ $CI=12000\{\frac{(108)^3-(100)^3}{(100)^3} \}$

On simplifying, we get,

$CI =Rs.\hspace{3}3116.54$

It can be clearly seen that the interest paid by Shruti (Rs. 3600) is more than that paid by Shalini (Rs. 3116.54).

To find by how much Shruti pays more than Shalini, subtract both the interests.

⇒ Interest paid by Shruti - Interest paid by Shalini

= 3600 - 3116.54

= Rs. 483.46

Therefore, for the given conditions, the interest paid by Shruti is more than that by Shalini by about Rs. 483.46.