Correct Option: C
Let the sum be P.
As, the interest is compounded half-yearly,
∴ R = 2%, T = 2 half years , A = ₹ 7,803
∴ A = P | 1 + | R | T | ||
100 |
⇒ 7803 = P | 1 + | 2 | 2 | ||
100 |
⇒ 7803 = P | 1 + | 1 | 2 | ||
50 |
⇒ 7803 = P × | 51 | × | 51 |
50 | 50 |
⇒ P = | 7803 × 50 × 50 | = ₹ 7500 |
51 × 51 |
- Aptitude
- Simple and compound interest
A) Rs. 7,000 |
B) Rs. 7,200 |
C) Rs. 7,500 |
D) Rs. 7,700 |
Correct Answer:
Description for Correct answer:
Rate % = 4 %,
time (t) = 1 year
Amount = Rs. 7803
When interest is compounded half-yearly
New Rate % =\( \Large \frac{4}{2} \) =2 %,
Time =\( \Large 1 \times 2 \)= 2 years
Required Rate % for 2 years CI
=\( \Large 2+2+\frac{2 \times 2}{100} \)=4.04 %
According to the question,
\( \Large\left(100+ 4.04\right)\) % of sum =Rs. 7803
Sum=\( \Large \frac{7803}{104.04} \times 100 \)=Rs. 7500
Part of solved Simple and compound interest questions and answers : >> Aptitude >> Simple and compound interest
Answer by Theo(12293) You can put this solution on YOUR website! |
A. Rs. 7000
B. Rs. 7200
C. Rs. 7500
D. Rs. 7700
Solution(By Examveda Team)
Time (t) = 1 years
Rate % = 4%
Amount = Rs. 7803
When interest is compounded half yearly
New Rate = $$\frac{4}{2}$$ = 2%
Time = 1 × 2 = 2 years
Required rate% for 2 years CI
$${\text{ = 2}} + {\text{2}} + \frac{{2 \times 2}}{{100}} = 4.04\% $$
According to question,
(100 + 4.04)%
of sum = Rs. 7803
$$\eqalign{ & \therefore {\text{Sum = }}\frac{{7803}}{{104.04}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}7500 \cr} $$
Q. A certain sum, invested at 4% per annum compound interest, compounded half yearly, amounts to 7803 Rs. at the end of one year. The sum is:
Answer: [B] Rs. 7500
Notes: Let the sum be P. As, the interest is compounded half-yearly, ∴ R = 2%, T = 2 half years $ \therefore A = P \left ( 1+\frac{R}{100} \right )^{T}$ $ => 7803 = P \left ( 1+\frac{2}{100} \right )^{2}$ $ => 7803 = P \left ( 1+\frac{1}{50} \right )^{2}$ $ => 7803 =
P\times \frac{51}{50}\times \frac{51}{50}$ $ => P = \frac{7803\times 50\times 50}{51\times 51} = 7500Rs$ Hence option [B] is correct answer.