# Compound Interest Quiz Set 006

### Question 1

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 2

Rs. 1224 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 4%?

A

Rs. 624.

B

Rs. 724.

C

Rs. 524.

D

Rs. 824.

Soln.
Ans: a

Let the parts P and (1224 - P). We have P × \$(1 + 4/100)^6\$ = (1224 - P) × \$(1 + 4/100)^7\$. Cancelling, we get P = (1224 - P) × (1 + 4/100). Simplifying, P = \${1224 × (100 + 4)}/(200 + 4)\$, which gives P = Rs. 624.

### Question 3

How much interest does an amount of Rs. 30000 earn @8% compounded annually for 2 years?

A

Rs. 4992.

B

Rs. 5092.

C

Rs. 4892.

D

Rs. 5192.

Soln.
Ans: a

Amount A = 30000 × \$(1 + 8/100)^2\$, which equals 30000 × \$108/100\$ × \$108/100\$ = 3 × 108 × 108 = Rs. 34992. So interest = A - P = 34992 - 30000 = Rs. 4992.

### Question 4

A bank offers an interest rate of 5% compounded annually. Initially I deposit Rs. 50000 in the bank under this scheme. After 1 year I again deposit Rs 50000. What is the total amount that I will get after 2 years?

A

Rs. 107625.

B

Rs. 107725.

C

Rs. 107525.

D

Rs. 107825.

Soln.
Ans: a

Let P, A, r and n have their usual meanings. For the first deposit n = 2, and for the second deposit n = 1. So total amount is P × \$((1 + r/100)^2 + (1 + r/100))\$ = \$P/10000\$ × \$((100 + r)^2 + 100(100 + r))\$ = \$P/10000 × (100 + r)\$ × \$(100 + r + 100)\$ which equals \${P × (100 + r) × (200 + r)}/10000.\$ Putting r = 5 and P = 50000 and cancelling 10000, we get 5 × 105 × 205 = Rs. 107625.

### Question 5

What is compound interest on Rs. 80000 after 2 years, invested at a rate of 6% compounded annually?

A

Rs. 9888.

B

Rs. 9988.

C

Rs. 9788.

D

Rs. 10088.

Soln.
Ans: a

The shortcut formula is CI = Pr(r + 200)/10000. Putting P = 80000, r = 6, we get \${80000 × 6 × (6 + 200)}/10000\$ = Rs. 9888.