# Compound Interest Quiz Set 016

### Question 1

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 2

The compound amount after 2 years on a principal of Rs. P is same as that on a principal of Rs. (606 - P) after 3 years, then what is P if the rate of interest is 2% p.a. compounded yearly?

A

Rs. 306.

B

Rs. 406.

C

Rs. 206.

D

Rs. 506.

Soln.
Ans: a

We have P × \$(1 + 2/100)^2\$ = (606 - P) × \$(1 + 2/100)^3\$. Cancelling, we get P = (606 - P) × (1 + 2/100). Simplifying, P = \${606 × (100 + 2)}/(200 + 2)\$, which gives P = Rs. 306.

### Question 3

The compound interest on a certain sum of money at 6% for a period of 2 years is Rs. 7416. What is the SI on this sum if the rate is halved, and time doubled?

A

Rs. 7200.

B

Rs. 7300.

C

Rs. 7100.

D

Rs. 7400.

Soln.
Ans: a

The shortcut formula is CI = Pr(r + 200)/10000. Putting CI = 7416, r = 6, we get 7416 = \${P × 6 × (6 + 200)}/10000\$. We can solve it to get P = Rs. 60000. The SI = P × (2 × t) × (r / 200) = P × t × (r / 100). Putting t = 2, r = 6 and P = 60000, we get SI = Rs. 7200.

### Question 4

How much interest does an amount of Rs. 30000 earn @9% compounded annually for 2 years?

A

Rs. 5643.

B

Rs. 5743.

C

Rs. 5543.

D

Rs. 5843.

Soln.
Ans: a

Amount A = 30000 × \$(1 + 9/100)^2\$, which equals 30000 × \$109/100\$ × \$109/100\$ = 3 × 109 × 109 = Rs. 35643. So interest = A - P = 35643 - 30000 = Rs. 5643.

### Question 5

How much interest does an amount of Rs. 9000000 earn @8% compounded annually for 3 years?

A

Rs. 2337408.

B

Rs. 2337508.

C

Rs. 2337308.

D

Rs. 2337608.

Soln.
Ans: a

Amount A = 9000000 × \$(1 + 8/100)^3\$, which equals 9000000 × \$108/100\$ × \$108/100\$ × \$108/100\$ = 9 × 108 × 108 × 108 = Rs. 11337408. So interest = A - P = 11337408 - 9000000 = Rs. 2337408. 