Compound Interest Quiz Set 003

Question 1

The compound amount after 3 years on a principal of Rs. x is same as that on a principal of Rs. (828 - x) after 4 years, then what is x if the rate of interest is 7% p.a. compounded yearly?

A

Rs. 428.

B

Rs. 528.

C

Rs. 328.

D

Rs. 628.

Soln.
Ans: a

We have x × $(1 + 7/100)^3$ = (828 - x) × $(1 + 7/100)^4$. Cancelling, we get x = (828 - x) × (1 + 7/100). Simplifying, x = ${828 × (100 + 7)}/(200 + 7)$, which gives x = Rs. 428.

Question 2

What is the difference in compound interest and simple interest on an amount of Rs. 60000 for a period of 2 years if the rate is 2% p.a. compounded annually?

A

Rs. 24.

B

Rs. 124.

C

Rs. 74.

D

Rs. 224.

Soln.
Ans: a

The shortcut formula for the difference between compound and simple interest over a period of 2 years is $Difference = Principal × (\text"rate"/100)^2$, which equals $(60000 × 2^2)/10000$ = Rs. 24.

Question 3

The compound amount after 3 years on a principal of Rs. x is same as that on a principal of Rs. (816 - x) after 4 years, then what is x if the rate of interest is 4% p.a. compounded yearly?

A

Rs. 416.

B

Rs. 516.

C

Rs. 316.

D

Rs. 616.

Soln.
Ans: a

We have x × $(1 + 4/100)^3$ = (816 - x) × $(1 + 4/100)^4$. Cancelling, we get x = (816 - x) × (1 + 4/100). Simplifying, x = ${816 × (100 + 4)}/(200 + 4)$, which gives x = Rs. 416.

Question 4

The compound amount after 2 years on a principal of Rs. P is same as that on a principal of Rs. (410 - P) after 3 years, then what is P if the rate of interest is 5% p.a. compounded yearly?

A

Rs. 210.

B

Rs. 310.

C

Rs. 110.

D

Rs. 410.

Soln.
Ans: a

We have P × $(1 + 5/100)^2$ = (410 - P) × $(1 + 5/100)^3$. Cancelling, we get P = (410 - P) × (1 + 5/100). Simplifying, P = ${410 × (100 + 5)}/(200 + 5)$, which gives P = Rs. 210.

Question 5

What is the amount receivable on Rs. 80000 after 6 months, invested at a rate of 8% compounded quarterly?

A

Rs. 83232.

B

Rs. 83332.

C

Rs. 83132.

D

Rs. 83432.

Soln.
Ans: a

In this case r = $8/4$% and n = 2 because compounding is quarterly. So A = 80000 × $(1 + 2/100)^2$, which equals 8 × 102 × 102, i.e., Rs. 83232.