Difference between compound interest and simple interest accrued on an amount of ₹ 18000 in 2 year

English

Gujarati

Hindi

6.Interest

hard

The difference between the compound interest and the simple interest accrued on an amount of ₹ $18000$ in $2$ years was ₹ $405 .$ What was the rate of interest per cent per annum?

A

$12$

B

$13$

C

$14$

D

$15$

Solution

Let rate of interest be $R \%$ p.a.

$S.I. =\frac{18000 \times 2 \times R}{100}$

$C.I. = 18000\left[\left(1+\frac{R}{100}\right)^{2}-1\right]$

$(2)-(1) \Rightarrow 18000\left[\left(1+\frac{R}{100}\right)^{2}-1-\frac{2 R}{100}\right]$

$=405 or 18000\left[\left(\frac{R}{100}\right)^{2}\right]$$=405$

Or $\left(\frac{R}{100}\right)^{2}=\frac{405}{18000}$

or $=\frac{45}{2000}$$=\frac{9}{400}$$\frac{R}{100} =\frac{3}{20}$

Or $R=15 \%$

Standard 13

Quantitative Aptitude

Share

Similar Questions

Divide $Rs. 2602$ between $X$ and $Y$, so that the amount of $X$ after $7 \,yr$ is equal to the amount of $Y$ after $9 \,yr$, the interest being compounded at $4 \%$ pa.

hard

A sum of ₹ $3,200$ invested at $10 \%$ per cent compounded quarterly amounts to ₹ $3,362.$ Compute the time period (In $years$)

medium

The difference between the simple interest and the compound interest (In ₹) on ₹ $600$ for $1$ year at $10 \%$ per annum, reckoned half-yearly is

medium

$A$ deposited $Rs. 6000$ in a bank at $5 \%$ per annum simple interest. $B$ deposited $Rs. 5000$ at $8 \%$ $p.a.$ compound interest. After $2$ years, the difference between their interests (In $Rs.$) will be

medium

Raghu invested a certain sum in Scheme $X$ for $4$ years.Scheme $X$ offers simple interest at $12$ per cent pa for the firsttwo years and compound interest (compounded annually) at $20$ per cent pa for the next two years. The total interest earned by him after $4$ years is ₹ $11016 .$ What was the sum (In ₹) invested by Raghu in Scheme $X ?$

medium