Question Detail
Find compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually
- Rs 312
- Rs 412
- Rs 512
- Rs 612
Answer: Option D
Explanation:
Please apply the formula
\begin{aligned}
Amount = P(1+\frac{R}{100})^n \\
\text{C.I. = Amount - P}
\end{aligned}
1. 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
2. A man saves Rs 200 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years.
- Rs 662
- Rs 662.01
- Rs 662.02
- Rs 662.03
Answer: Option C
Explanation:
\begin{aligned}
[200(1+\frac{5}{100})^3 + 200(1+\frac{5}{100})^2+ \\ 200(1+\frac{5}{100})]
= [200(\frac{21}{20} \times \frac{21}{20} \times \frac{21}{20})\\
+ 200(\frac{21}{20}\times\frac{21}{20})+200(\frac{21}{20})] \\
= 662.02
\end{aligned}
3. 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}
4. We need to divide Total Sum Rs. 3364 between Ram and Sham so that Ram's share at the end of 5 years may equal to Sham's share at the end of seven years with compound interest rate at 5 percent.
- 1864 and 1500
- 1764 and 1600
- 1664 and 1700
- 1564 and 1800
Answer: Option B
Explanation:
It is clear from question that Ram's share after five years = Sham's share after seven years
Hence we can conclude following :
\begin{aligned}
\text{(Rams's present share)}\left(1 + \dfrac{5}{100}\right)^5 = \text{(Sham's present share)}\left(1 + \dfrac{5}{100}\right)^7\\
=> \dfrac{\text{(Ram's present share)}}{\text{(Sham's present share)}}= \dfrac{\left(1 + \dfrac{5}{100}\right)^7}{\left(1 + \dfrac{5}{100}\right)^5} \\ = \left(1 + \dfrac{5}{100}\right)^{(7-5)} = \left(1 + \dfrac{5}{100}\right)^2 \\ = \left(\dfrac{21}{20}\right)^2 = \dfrac{441}{400}
\end{aligned}
Ram's present share : B's present share = 441 : 400
\begin{aligned}
\text{As amount is Rs.3364, Ram's share = }3364 \times \dfrac{441}{(441+400)} \\\\
= 3364 \times \dfrac{441}{841} = 4 \times 441 = \text{ Rs. 1764}
\end{aligned}
So Sham's share is = 3364-1764 = 1600
5. 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}