Find the compound interest on Rs (7500 at 4% per annum for 2 years, compounded annually)

Find the amount of compound interest for Rs 7500 for 1 year at 8% per annum compounded half-yearly.

Answer

Hint: In this question it is given that we have to find the amount of compound interest for Rs 7500 for 1 year at 8% per annum compounded half-yearly. So to solve this kind of problem we need know that,
Amount= $$A=P\left( 1+\dfrac{R}{100} \right)^{nt} $$......(1)
Where,
A=Final amount
P=Principle amount
R=Rate of interest
n=Number of times interest applied per time period
t=Number of time periods elapsed
Complete step-by-step solution:
Given data,
P=7500, R=8, n= 2 half-yearly= 2 times, t= 1 year=1
Therefore, Final amount,
$$A=P\left( 1+\dfrac{R}{100} \right)^{nt} $$
  =$$7500\left( 1+\dfrac{8}{100} \right)^{2\times 1} $$
  =$$7500\left( 1+\dfrac{2}{25} \right)^{2} $$
  =$$7500\left( \dfrac{25+2}{25} \right)^{2} $$
  =$$7500\left( \dfrac{27}{25} \right)^{2} $$
  =$$7500\times \dfrac{27}{25} \times \dfrac{27}{25}$$
  =$$12\times 27\times 27$$
  = 8784.
Therefore, the amount is Rs 8784.
And the compound interest = (A - P) = Rs(8784 - 7500) = Rs 1248
Note: While solving this type of problems, always remember that the value of n is the total number of times where each time the amount is compounded and the term might be a whole year, half-year or a quarter-year etc.

Question Detail

• Rs. 610
• Rs. 612
• Rs. 614
• Rs. 616

Answer: Option B

Explanation:

\begin{aligned}
Amount = [7500 \times (1+ \frac{4}{100})^2] \\
= (7500 \times \frac{26}{25} \times \frac{26}{25}) \\
= 8112 \\

\end{aligned}

So compound interest = (8112 - 7500) = 612

Similar Questions :

1. Albert invested amount of 8000 in a fixed deposit for 2 years at compound interest rate of 5 % per annum. How much Albert will get on the maturity of the fixed deposit.

• Rs. 8510
• Rs. 8620
• Rs. 8730
• Rs. 8820

Answer: Option D

Explanation:

\begin{aligned}
=> (8000 \times(1+\frac{5}{100})^2) \\
=> 8000 \times \frac{21}{20}\times \frac{21}{20} \\
=> 8820
\end{aligned}

2. 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%

3. 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}

4. 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}

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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