Question

What sum will amount to Rs.6,600 in 4 years at $8\%$ per annum at simple interest?

A) Rs 6,000

B) Rs 5,000

C) Rs 4,000

D) Rs 6,200

Answer 1

Hint: Assume that the sum which will amount to Rs 6,600 in 4 years @ 8% per annum be P. Use the fact that the interest on an amount P for time t years at the rate of r% per annum is given by $I=\dfrac{P\times r\times t}{100}$ and amount is given by $A=I+P$. Equate the amount to $6600$ and hence form an equation in P. Solve for P. Hence find the sum which will amount to Rs 6,600 in the above-mentioned conditions.

Complete step-by-step answer:

Let the sum which will amount to Rs 6,600 in 4 years @ 8% per annum be P.

We know that the interest on the amount P for time t years @ r% per annum is given by $I=\dfrac{P\times r\times t}{100}$

Hence, we have

$I=\dfrac{P\times 8\times 4}{100}=\dfrac{8P}{25}$

We know that the amount A is given by $A=I+P$

Hence, we have

$A=\dfrac{8P}{25}+P=\dfrac{33P}{25}$

But given that A = 6600

Hence, we have

$\dfrac{33P}{25}=6600$

Multiplying both sides by 25, we get

$33P=25\times 6600$

Dividing both sides by 33, we get

$P=\dfrac{25\times 6600}{33}=25\times 200=5000$

Hence the sum which will amount to Rs 6,600 @ 8% per annum for 4 years at simple interest is Rs. 5000.

Hence option (B) is correct.

Note:

Verification:

We have P = 5000, r = 8% and t = 4 years

Hence, we have

$I=\dfrac{5000\times 8\times 4}{100}=1600$

Hence, we have A = P+I = 5000+1600 = Rs 6,600

Hence our answer is verified to be correct.