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Compound Interest

Q1. A sum of money placed at C.I. double itself in 5 years. It will amount to eight times itself at the same rate of interest in ___________ years.

(a) 10 (b) 15 (c) 16 (d) 20

Solution.
(x1)1/(n1) = (x2)1/(n2)

(2)1/5 = (8)1/(n2)

(2)1/5 = (2)3/(n2)

n2 = 15
Solution

Q2. If interest is calculated on interest, it is example of compound interest. (True/False)

Solution.
True .
Solution

Q3. The population of a town at the beginning of the year 2001 was 1,75,000 . If the rate of increase be 52 per thousand of the population . find the populaton at the beginning of the year 2006 .

Solution.
A = p(1 +
r/100
)n

A = 1,75,000 (1 +
5.2/100
)5 = 1,75,000(1.052)5

A = 1,75,000 (1.2884830) = 2,25,485
Solution

Q4. The least number of complete years in which a sum of money put out at 20% C.I will be more than doubled in _________ years .

(a) 7 (b) 3 (c) 4 (d) 5

Solution.
(c) 4
Solution

Q5. Which investment is better , 5% per annum compounded quarterly or 5.12% per annum .

Solution.
effective = (1 +
0.05/4
)4 - 1 = (1.0125)4 - 1

= 1.05095 - 1 = 0.05095

effective = 5.095 % per annum.

so, 5.12 % is better investment .
Solution

Q6. On a specific money the ratio of CI for 3 year and 2 year is 21:20 respectively, find the rate of interest .

Solution.
21 x = P(1 +
r/100
)3 ⇒ 20x = P(1 +
r/100
)2

21/20
= 1 +
r/100
⇒
r/100
=
1/20
⇒ r = 5%
Solution

Q7. A sum of money becomes
36/25
times in 2 years find the rate of CI .

Solution.
A = P(1 +
r/100
)n ⇒
36P/25
= P(1 +
r/100
)2

6/5
= 1 +
r/100
⇒
1/5
=
r/100
⇒ r = 20%
Solution

Q8. A sum of money of CI amount to Rs. 2750 in 2 years and amount Rs. 3125 in 3 years . find the sum .

(a) 2129 (b) 3000 (c) 4200 (d) 3900

Solution.
Sum = A1(A1/A2)n

= (2750)(22/25)2

= 2129.6
Solution

Q9. A what rate of CI does a sum of money become 16/9 time itself in 2 years .

(a) 33.3% (b) 12% (c) 22% (d) 14%

Solution.
A = P(1 + r/100)n

16P/9 = P(1 + r/100)2

4/3 = 1 + r/100

r = 33.3%
Solution

Q10. If the CI on a certain sum of money for 2 years at 5% is Rs.190, find the SI at the same rate of the same time .

(a) 145.6 (b) 160 (c) 185.3 (d) 190

Solution.
SI =
200r/r(r + 200)
x CI

SI =
200 x 5 x 190/5 x 205


=
190000/1025


= 185.3
Solution