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Question Detail
Effective annual rate of interest corresponding to nominal rate of 6% per annum compounded half yearly will be
- 6.09%
- 6.10%
- 6.12%
- 6.14%
Answer: Option A
Explanation:
Let the amount Rs 100 for 1 year when compounded half yearly, n = 2, Rate = 6/2 = 3%
\begin{aligned}
Amount = 100(1+\frac{3}{100})^2 = 106.09
\end{aligned}
Effective rate = (106.09 - 100)% = 6.09%
1. Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is
- Rs 1650
- Rs 1750
- Rs 1850
- Rs 1950
Answer: Option B
Explanation:
\begin{aligned}
C.I. = (4000 \times(1+\frac{10}{100})^2 - 4000) \\
= 4000 * \frac{11}{10} * \frac{11}{10} - 4000 \\
= 840 \\
\text{So S.I. = } \frac{840}{2} = 420\\
\text{So Sum = } \frac{S.I. * 100}{R*T} \\
= \frac{420 * 100}{3*8} \\
= Rs 1750
\end{aligned}
2. Find the compound interest on Rs.16,000 at 20% per annum for 9 months, compounded quarterly
- Rs 2520
- Rs 2521
- Rs 2522
- Rs 2523
Answer: Option C
Explanation:
Please remember, when we have to calculate C.I. quarterly then we apply following formula if n is the number of years
\begin{aligned}
Amount = P(1+\frac{\frac{R}{4}}{100})^{4n}
\end{aligned}
Principal = Rs.16,000;
Time=9 months = 3 quarters;
Rate = 20%, it will be 20/4 = 5%
So lets solve this question now,
\begin{aligned}
Amount = 16000(1+\frac{5}{100})^3 \\
= 18522\\
C.I = 18522 - 16000 = 2522
\end{aligned}
3. In what time will Rs.1000 become Rs.1331 at 10% per annum compounded annually
- 2 Years
- 3 Years
- 4 Years
- 5 Years
Answer: Option B
Explanation:
Principal = Rs.1000;
Amount = Rs.1331;
Rate = Rs.10%p.a.
Let the time be n years then,
\begin{aligned}
1000(1+\frac{10}{100})^n = 1331 \\
(\frac{11}{10})^n = \frac{1331}{1000} \\
(\frac{11}{10})^3 = \frac{1331}{1000} \\
\end{aligned}
So answer is 3 years
4. What will be the difference between simple and compound interest @ 10% per annum on the sum of Rs 1000 after 4 years
- Rs 62.10
- Rs 63.10
- Rs 64.10
- Rs 65.10
Answer: Option C
Explanation:
\begin{aligned}
S.I. = \frac{1000*10*4}{100} = 400 \\
C.I. = [1000(1+\frac{10}{100})^4 - 1000] \\
= 464.10
\end{aligned}
So difference between simple interest and compound interest will be 464.10 - 400 = 64.10
5. At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years
- 3%
- 4%
- 5%
- 6%
Answer: Option D
Explanation:
Let Rate will be R%
\begin{aligned}
1200(1+\frac{R}{100})^2 = \frac{134832}{100} \\
(1+\frac{R}{100})^2 = \frac{134832}{120000} \\
(1+\frac{R}{100})^2 = \frac{11236}{10000} \\
(1+\frac{R}{100}) = \frac{106}{100} \\
=> R = 6\%
\end{aligned}
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