model 1 basic compound interest using formula Practice Questions Answers Test with Solutions & More Shortcuts

Question : 6 [SSC Sub-Inspector 2012]

The compound interest on Rs.30,000 at 7% per annum for a certain time is Rs.4,347. The time is

a) 2.5 years

b) 3 years

c) 2 years

d) 4 years

Answer: (c)

Using Rule 1,

A = P$(1 + R/100)^T$

30000 + 4347 = $30000(1 + 7/100)^T$

$34347/30000 = (107/100)^T$

$11449/10000 = (107/100)^2 = (107/100)^T$

Time = 2 years

Question : 7 [SSC CGL Prelim 2008]

A certain sum amounts to Rs.5,832 in 2 years at 8% per annum compound interest, the sum is

a) Rs.5,400

b) Rs.5,000

c) Rs.5,280

d) Rs.5,200

Answer: (b)

Using Rule 1,

5832 = P$(1 + 8/100)^2$

5832 = P$(1 + 2/25)^2$

5832 = P $× 27/25 × 27/25$

P = ${5832 × 25 × 25}/{27 × 27}$ = Rs.5000

Question : 8 [SSC CPO S.I.2007]

The compound interest on Rs.8,000 at 15% per annum for 2 years 4 months, compounded annually is:

a) Rs.3100

b) Rs.2980

c) Rs.3109

d) Rs.3091

Answer: (c)

Using Rule 1,

Amount = P$(1 + R/100)^t$

= 8000$(1 + 15/100)^{2{1}/3}$

= 8000$(1 + 3/20)^2(1 + 3/{20 × 3})$

= $8000 × 23/20 × 23/20 × 21/20$ = Rs.11109

Compound Interest

= Rs.(11109 - 8000) = Rs.3109.

Question : 9 [SSC CPO S.I.2008]

The compound interest on Rs.6,000 at 10% per annum for 1$1/2$ years, when the interest being compounded annually, is

a) Rs.900

b) Rs.910

c) Rs.930

d) Rs.870

Answer: (c)

Amount = 6000$(1 + 10/100) × (1 + {{1/2} × 10}/100)$

= $6000 × 11/10 × 21/20$ = Rs.6930

Using Rule 4,
If the time is in fractional form i.e.,t = nF, then
A = P$(1 + r/100)^n(1 + {rF}/100)$e.g. t =3$5/7$ yrs, then
A = P$(1 + r/100)^3(1 + r/100 × 5/7)$

Here, t = nF

A = P$(1 + r/100)^n(1 + {rF}/100)$

CI = Rs.(6930 - 6000) = Rs.930

Question : 10 [SSC CISF ASI 2010]

A sum becomes Rs.1,352 in 2 years at 4% per annum compound interest. The sum is

a) Rs.1,250

b) Rs.1,225

c) Rs.1,245

d) Rs.1,270

Answer: (a)

Using Rule 1,

Let the sum be Rs.x.

1352 = $x(1 + 4/100)^2$

1352 = $x(1 + 1/25)^2$

$1352 = x(26/25)^2$

$x = {1352 × 25 × 25}/{26 × 26}$ = Rs.1250

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