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Question Detail
The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Rs 1. Find the sum
- Rs 600
- Rs 625
- Rs 650
- Rs 675
Answer: Option B
Explanation:
Let the Sum be P
\begin{aligned}
S.I. = \frac{P*4*2}{100} = \frac{2P}{25}\\
C.I. = P(1+\frac{4}{100})^2 - P \\
= \frac{676P}{625} - P \\
= \frac{51P}{625} \\
\text{As, C.I. - S.I = 1}\\
=> \frac{51P}{625} - \frac{2P}{25} = 1 \\
=> \frac{51P - 50P}{625} = 1 \\
P = 625
\end{aligned}
1. If the simple interest on a sum of money for 2 years at 5% per annum is Rs.50, what will be the compound interest on same values
- Rs.51.75
- Rs 51.50
- Rs 51.25
- Rs 51
Answer: Option C
Explanation:
\begin{aligned}
S.I. = \frac{P*R*T}{100} \\
P = \frac{50*100}{5*2} = 500\\
Amount = 500(1+\frac{5}{100})^2 \\
500(\frac{21}{20} * \frac{21}{20}) \\
= 551.25 \\
C.I. = 551.25 - 500 = 51.25
\end{aligned}
2. The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Rs 1. Find the sum
- Rs 600
- Rs 625
- Rs 650
- Rs 675
Answer: Option B
Explanation:
Let the Sum be P
\begin{aligned}
S.I. = \frac{P*4*2}{100} = \frac{2P}{25}\\
C.I. = P(1+\frac{4}{100})^2 - P \\
= \frac{676P}{625} - P \\
= \frac{51P}{625} \\
\text{As, C.I. - S.I = 1}\\
=> \frac{51P}{625} - \frac{2P}{25} = 1 \\
=> \frac{51P - 50P}{625} = 1 \\
P = 625
\end{aligned}
3. 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%
4. A sum of money invested at compound interest to Rs. 800 in 3 years and to Rs 840 in 4 years. The rate on interest per annum is.
- 4%
- 5%
- 6%
- 7%
Answer: Option B
Explanation:
S.I. on Rs 800 for 1 year = 40
Rate = (100*40)/(800*1) = 5%
5. 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
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