# Compound Interest Quiz Set 010

### Question 1

The compound interest on a certain sum of money at 6% for a period of 2 years is Rs. 8652. What is the SI on this sum if the rate is halved, and time doubled?

A

Rs. 8400.

B

Rs. 8500.

C

Rs. 8300.

D

Rs. 8600.

Soln.
Ans: a

The shortcut formula is CI = Pr(r + 200)/10000. Putting CI = 8652, r = 6, we get 8652 = \${P × 6 × (6 + 200)}/10000\$. We can solve it to get P = Rs. 70000. The SI = P × (2 × t) × (r / 200) = P × t × (r / 100). Putting t = 2, r = 6 and P = 70000, we get SI = Rs. 8400.

### Question 2

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 3

The difference between compound interest(annual compounding) and simple interest for a period of 2 years is Rs. 28. What is the rate p.a. if principal is Rs. 70000?

A

2%.

B

4%.

C

3%.

D

5%.

Soln.
Ans: a

If d is the difference, r is the rate and P is the principal, then the shortcut formula for the difference between compound and simple interest over a period of 2 years is d = P × \$(r/100)^2\$. So rate = 100 × \$√{d/P}\$ = 100 × \$√{28/70000}\$ = 2%.

### Question 4

An amount P is invested for 1 year @2% p.a. The simple interest is Rs. 3000. What would be the compound interest on the same amount, at the same rate and for the same time, compounded annually?

A

Rs. 3000.

B

Rs. 3100.

C

Rs. 2900.

D

Rs. 3200.

Soln.
Ans: a

The compound interest and simple interest are exactly same for a period of 1 year if P and r are always same.

### Question 5

An amount P is invested for 2 years @7% p.a. The simple interest is Rs. 6000. What would be the compound interest on the same amount, at the same rate and for the same time, compounded annually?

A

Rs. 6210.

B

Rs. 6310.

C

Rs. 6110.

D

Rs. 6410.

Soln.
Ans: a

Let SI, P, r, t have usual meanings. Then, for 2 years, SI = (P × r × 2)/100. So P = \$(50 × SI)/r\$. The compound interest for 2 years by shortcut formula is \${P × r × (200 + r)}/10000\$. Putting P here, it becomes, \${{(50 × SI)/r} × r × (200 + r)}/10000\$ = \${SI × (r + 200)}/200\$ = \${6000 × (7 + 200)}/200\$ = Rs. 6210. 