A certain sum at compound interest amounts in | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the principal be $P$ and the rate of interest be $R \%$. The amount after $n$ years is given by $A = P(1 + \frac{R}{100})^n$. For $2$ years: $

Vedclass · Accepted Answer

$2500$

Vedclass · Answer

(C) Let the principal be $P$ and the rate of interest be $R \%$. The amount after $n$ years is given by $A = P(1 + \frac{R}{100})^n$. For $2$ years: $2809 = P(1 + \frac{R}{100})^2$  --- $(i)$ For $3$ years: $2977.54 = P(1 + \frac{R}{100})^3$  --- $(ii)$ Dividing $(ii)$ by $(i)$: $\frac{2977.54}{2809} = 1 + \frac{R}{100}$ $1.06 = 1 + \frac{R}{100}$ $\frac{R}{100} = 0.06 \implies R = 6 \%$. Now,substitute $R = 6$ in equation $(i)$: $2809 = P(1 + \frac{6}{100})^2$ $2809 = P(1.06)^2$ $2809 = P(1.1236)$ $P = \frac{2809}{1.1236} = 2500$. Thus,the rate of interest is $6 \%$ and the original sum is ₹ $2500$.

$A$ certain sum at compound interest amounts in two years to ₹ $2809$ and in three years to ₹ $2977.54$. Find the rate of interest and the original sum (in ₹).

Similar Questions

Amit invested an amount of $Rs. 25000$ in a fixed deposit at a compound interest rate of $8 \%$ per annum for $2$ years. What amount (in $Rs.$) will Amit receive at the end of the period?

$A$ sum of money placed at compound interest doubles itself in $5$ years. It will amount to eight times itself at the same rate of interest in (in $years$):

$A$ sum of ₹ $1260$ is borrowed from a money lender at $10 \%$ p.a. compounded annually. If the amount is to be paid back in two equal annual instalments,find out the annual instalment (in ₹).

At what rate per cent compound interest does a sum of money become $16$ times in $4$ years?

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 $4 \%$ per annum.

Vedclass Test Series

Exam Paper Generator

Online Exam Module