A sum of money lent at compound interest for | vedclass

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

Question

(A) Let the principal be $P$.When interest is compounded half-yearly,the rate $R = 20/2 = 10 \% \, p.a.$ and time $T = 2 	imes 2 = 4$ half-years.$CI_

Vedclass · Accepted Answer

$40000$

Vedclass · Answer

(A) Let the principal be $P$.When interest is compounded half-yearly,the rate $R = 20/2 = 10 \% \, p.a.$ and time $T = 2 	imes 2 = 4$ half-years.$CI_{half-yearly} = P \left[ (1 + 10/100)^4 - 1 ight] = P \left[ (1.1)^4 - 1 ight] = P (1.4641 - 1) = 0.4641 P$.When interest is compounded annually,the rate $R = 20 \% \, p.a.$ and time $T = 2$ years.$CI_{annually} = P \left[ (1 + 20/100)^2 - 1 ight] = P \left[ (1.2)^2 - 1 ight] = P (1.44 - 1) = 0.44 P$.According to the question,the difference is $Rs. 964$:$0.4641 P - 0.44 P = 964$$0.0241 P = 964$$P = 964 / 0.0241 = 40000$.Thus,the sum is $Rs. 40000$.

$A$ sum of money lent at compound interest for $2 \, yr$ at $20 \% \, p.a.$ would fetch $Rs. 964$ more,if the interest was payable half-yearly than if it was payable annually. What is the sum (in $Rs.$)?

Similar Questions

The population of a state increases by $10 \%$ every year. If its population in the year $2003$ was $15$ lakhs,what was its population in the year $2005$ (in lakhs)?

Find the difference between $C.I.$ and $S.I.$ on $Rs. 15000$ at $3 \%$ per annum for $3$ years.

What would be the $C.I.$ obtained on an amount of $12500$ at the rate of $12 \, p.c.p.a.$ after $2$ years (in $Rs.$)?

What will be the compound interest (in ₹) on a sum of ₹ $1875$ after $2$ years if the rate of interest for the first year is $4 \%$ and that for the second year is $8 \%$?

If the compound interest on a certain sum for $2$ years is ₹ $60.60$ and the simple interest is ₹ $60$,then the rate of interest per annum (in $\%$) is

Vedclass Test Series

Exam Paper Generator

Online Exam Module