19. The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is :
a. 3
b. 4
c. 5
d. 6
Answer: B
Explanation:
Let the sum be \(p\).
\( \Rightarrow p{\left( {1 + \dfrac{{20}}{{100}}} \right)^n} = 2p\)
\( \Rightarrow {\left( {\dfrac{6}{5}} \right)^n} = 2\)
Here it is difficult to solve. So to simplify it, we take log on both sides
\( \Rightarrow \log {\left( {\dfrac{6}{5}} \right)^n} = \log 2\)
\( \Rightarrow n\left( {\log 6 - \log 5} \right) = \log 2\)
\( \Rightarrow n = \dfrac{{\log 2}}{{\left( {\log 6 - \log 5} \right)}} = 3.8017\)
So it will take nearly 4 years to become double.
Shortcut Technique:
The number of years to take a certain amount of money to become double is \(t\) at \(r%\) then \(r \times t = 72\)
This technique you can find in any MBA finance text book. This formula gives you only approximate value.
So \(t = \dfrac{{72}}{{20}} = 3.6\) years
20. The compound interest on Rs.2800 for $1\displaystyle\frac{1}{2}$years at 10% per annum is :
a. Rs.441.35
b. Rs.436.75
c. Rs.434
d. Rs.420
21. If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is :
a. Rs.8082
b. Rs.7800
c. Rs.8100
d. Rs.8112
22. A sum amounts to Rs.2916 in 2 years and to Rs.3149.28 in 3 years at compound interest. The sum is :
a. Rs.1500
b. Rs.2000
c. Rs.2500
d. Rs.3000
Answer: C
Explanation:
Let P be the principal and R% per annum be rate.
Then P ${{{\left( {1 + \displaystyle\frac{R}{{100}}} \right)}^3}}$=3149.28 ........ (i)
and P ${{{\left( {1 + \displaystyle\frac{R}{{100}}} \right)}^2}}$=2916 ..........(ii)
On dividing (i) and (ii) we get
${\left( {1 + \displaystyle\frac{R}{{100}}} \right)}$ = $\displaystyle\frac{{3149.28}}{{2916}}$
or ${100 = \displaystyle\frac{{233.28}}{{2916}}}$ or R = $\displaystyle\frac{{233.28}}{{2916}} \times 100 = 8\% $
Now P ${\left( {1 + \displaystyle\frac{8}{{100}}} \right)^2} = 2916$
or P $ \times \displaystyle\frac{{27}}{{25}} \times \displaystyle\frac{{27}}{{25}} = 2916$
or P = $\displaystyle\frac{{2916 \times 25 \times 25}}{{27 \times 27}}$=Rs. 2500
23. A sum of money amounts to Rs.10648 in 3 years and Rs.9680 in 2 years. The rate of interest is :
a. 5%
b. 10%
c. 15%
d. 20%
Answer: B
Explanation:
Let P be the principal and R% annum be the rate. Then.
P ${\left( {1 + \displaystyle\frac{R}{{100}}} \right)^3} = 10648$ - - - (i)
and P ${\left( {1 + \displaystyle\frac{R}{{100}}} \right)^2} = 9680$ - - - (ii)
On dividing (i) by (ii), we have
$\left( {1 + \displaystyle\frac{R}{{100}}} \right) = \displaystyle\frac{{10648}}{{9680}}$
or $\displaystyle\frac{R}{{100}} = \displaystyle\frac{{968}}{{9680}} = \displaystyle\frac{1}{{10}}$
or R = $\displaystyle\frac{1}{{10}} \times 100 = 10\% $
24. The difference between simple interest and compound interest at the same rate for Rs.5000 for 2 years is Rs.72. The rate of interest is :
a. 10%
b. 12%
c. 6%
d. 8%
