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

#### compound interest PRACTICE TEST [6 - EXERCISES]

Question : 1 [SSC CGL Tier-I 2013]

The time in which Rs.80,000 amounts to Rs.92,610 at 10% p.a. compound interest, interest being compounded semi annually is :

a) 3 years

b) 1\$1/2\$ years

c) 2\$1/2\$ years

d) 2 years

Using Rule 1 and 2,

Time = t half year

and R = 5% per half year

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

\$92610/80000 = (1 + 5/100)^T\$

\$9261/8000 = (21/20)^T\$

T = 3 half years or 1\$1/2\$ years

\$(21/20)^3 = (21/20)^T\$

Question : 2 [SSC CPO S.I.2006]

If the rate of interest be 4% per annum for first year, 5% per annum for second year and 6% per annum for third year, then the compound interest of Rs.10,000 for 3 years will be

a) Rs.2,000

b) Rs.1,600

c) Rs.1,575.20

d) Rs.1,625.80

Using Rule 3,
If there are distinct 'rates of interest' for distinct time periods i.e.,
Rate for 1st year → \$r_1\$%
Rate for 2nd year → \$r_2\$%
Rate for 3rd year → \$r_3\$% and so on
Then A = P\$(1 + r_1/100)(1 + r_2/100)(1 + r_3/100)\$...
C.I. = A - P

Amount = P\$(1 + R_1/100)(1 + R_2/100)(1 + R_3/100)\$

= 10000\$(1+ 4/100)(1 + 5/100)(1 + 6/100)\$

= \$10000 × 26/25 × 21/20 × 53/50\$

A = Rs.11575.2

C.I. = Rs.(11575.2–10000) = Rs.1575.2

Question : 3 [SSC CGL Tier-I 2010]

In how many years will a sum of Rs.800 at 10% per annum compound interest, compounded semi-annually becomes Rs.926.10 ?

a) 2\$1/2\$ years

b) 1\$1/2\$ years

c) 2\$1/3\$ years

d) 1\$2/3\$ years

Using Rule 1 and 2,

Rate = 10% per annum = 5% half yearly

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

926.10 = 800\$(1 + 5/100)^T\$

\$9261/8000 = (21/20)^T\$

\$(21/20)^3 = (21/20)^T\$

Time = 3 half years = 1\$1/2\$ years

Question : 4 [SSC CGL Tier-I 2010]

At what rate per cent per annum will a sum of Rs.1,000 amounts to Rs.1,102.50 in 2 years at compound interest ?

a) 6.5%

b) 5%

c) 6%

d) 5.5%

Using Rule 1,

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

Let rate be 'r'

\${1102.50}/1000 = (1 + r/100)^2\$

\$11025/10000 = (1 + r/100)^2\$

\$(105/100)^2 = (1 + r/100)^2\$

1 + \$r/100 = 105/100\$

\$r/100 = 5/100\$ = 5%

Question : 5 [SSC CGL Prelim 2003]

In what time will Rs.1000 amounts to Rs.1331 at 20% per annum, compounded half yearly ?

a) 2\$1/2\$ years

b) 1\$1/2\$ years

c) 1 year

d) 2 years

Using Rule 1 and 2,

Let the required time be t years. Interest is compounded half yearly.

Time = 2t half years and rate

= \$20/2\$ = 10%

1000\$(1 + 10/100)^{2t}\$ = 1331

\$(11/10)^{2t} = 1331/1000\$

\$(11/10)^{2t} = (11/10)^3\$ ⇒ 2t = 3

t = \$3/2\$ years or 1\$1/2\$ years

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