# Compound Interest Quiz Set 018

### Question 1

Rs. 808 is divided into parts such that the compound amount on first part after 6 years is same as that for the other part after 7 years. What is the first part if the rate of interest in both the cases is 2%?

A

Rs. 408.

B

Rs. 508.

C

Rs. 308.

D

Rs. 608.

Soln.
Ans: a

Let the parts P and (808 - P). We have P × $(1 + 2/100)^6$ = (808 - P) × $(1 + 2/100)^7$. Cancelling, we get P = (808 - P) × (1 + 2/100). Simplifying, P = ${808 × (100 + 2)}/(200 + 2)$, which gives P = Rs. 408.

### Question 2

What is compound interest on Rs. 90000 after 2 years, invested at a rate of 3% compounded annually?

A

Rs. 5481.

B

Rs. 5581.

C

Rs. 5381.

D

Rs. 5681.

Soln.
Ans: a

The shortcut formula is CI = Pr(r + 200)/10000. Putting P = 90000, r = 3, we get ${90000 × 3 × (3 + 200)}/10000$ = Rs. 5481.

### Question 3

The compound interest on a certain sum of money at 3% for a period of 2 years is Rs. 5481. What is the SI on this sum if the rate is halved, and time doubled?

A

Rs. 5400.

B

Rs. 5500.

C

Rs. 5300.

D

Rs. 5600.

Soln.
Ans: a

The shortcut formula is CI = Pr(r + 200)/10000. Putting CI = 5481, r = 3, we get 5481 = ${P × 3 × (3 + 200)}/10000$. We can solve it to get P = Rs. 90000. The SI = P × (2 × t) × (r / 200) = P × t × (r / 100). Putting t = 2, r = 3 and P = 90000, we get SI = Rs. 5400.

### Question 4

The compound interest on a certain sum of money at 5% for a period of 2 years is Rs. 3075. What is the SI on this sum if the rate is halved, and time doubled?

A

Rs. 3000.

B

Rs. 3100.

C

Rs. 2900.

D

Rs. 3200.

Soln.
Ans: a

The shortcut formula is CI = Pr(r + 200)/10000. Putting CI = 3075, r = 5, we get 3075 = ${P × 5 × (5 + 200)}/10000$. We can solve it to get P = Rs. 30000. The SI = P × (2 × t) × (r / 200) = P × t × (r / 100). Putting t = 2, r = 5 and P = 30000, we get SI = Rs. 3000.

### Question 5

What is the difference in compound interest and simple interest on an amount of Rs. 40000 for a period of 2 years if the rate is 7% p.a. compounded annually?

A

Rs. 196.

B

Rs. 296.

C

Rs. 246.

D

Rs. 396.

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 $(40000 × 7^2)/10000$ = Rs. 196. 