What sum invested at 4% per annum compounded semi annually amounts to 7803 at the end of the one year?

Correct Option: C

Let the sum be P.
As, the interest is compounded half-yearly,
∴ R = 2%, T = 2 half years , A = ₹ 7,803

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Solution(By Examveda Team)
What sum invested at 4% per annum compounded semi annually amounts to 7803 at the end of the one year?
What sum invested at 4% per annum compounded semi annually amounts to?
What sum invested for 1 years compounded half yearly at the rate of 4% pa will amount to 132651?
On what sum will the compound interest for 2 years at 4% per annum be 75712?

∴ 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

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Question 204162: A certain sum invested at 4% per annum compounded semi-annually amounts to $7803 after one year. Find the sum.
Answer by Theo(12293)

(Show Source):

You can put this solution on YOUR website!
The formula that you need is:
Present Value of a Future Amount =
FA = future amount = $7803.
n = 2 halves of a one year = 2
i = interest rate per half of a year = 4% / 2 / 100% = .02
-----
Present Value of a Future Amount becomes:
7803/(1.02)^2 = 7500 = $7,500.00
-----
You invested $7,500.00 at the start of the year.
At the end of the first half you had 7500 * 1.02 = 7650 = $7,650.00
At the end of the second half you had 6750 * 1.02 = 7803 = $7,803.00
-----

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.