7
A sum of Rs. 2000 at 40% per annum compounded annually. Calculate the interest for the third year at compound interest.
- A1500
- B1600
- C1568
- D1750
Answer not set
Discussion 1
Log in or create a free account to reply and vote.
0
CCommunity
We know the formula for compound interest -
$(\Rightarrow {\bf{CI}}\; = \;\left[ {{\bf{P}}\left\{ {{{\left( {1\; + \;\frac{{\bf{R}}}{{100}}} \right)}^t} - 1} \right\}} \right])$
Where,
CI = Compound interest
P = Principal
R = Rate of interest
t = Time period
RequiredCI $(= {\rm{\;}}\left[ {2000\left\{ {{{\left( {1\; + \;\frac{{40}}{{100}}} \right)}^3} - 1} \right\}} \right]{\rm{\;}} = {\rm{\;Rs}}.3488)$
Required CI for 2 years $(= \;\left[ {2000\left\{ {{{\left( {1\; + \;\frac{{40}}{{100}}} \right)}^2} - 1} \right\}} \right]{\rm{\;}} = {\rm{\;Rs}}.1920)$
Interest for the third year = 3488 – 1920 = Rs. 1568
∴ Interest for the third year = Rs. 1568
$(\Rightarrow {\bf{CI}}\; = \;\left[ {{\bf{P}}\left\{ {{{\left( {1\; + \;\frac{{\bf{R}}}{{100}}} \right)}^t} - 1} \right\}} \right])$
Where,
CI = Compound interest
P = Principal
R = Rate of interest
t = Time period
RequiredCI $(= {\rm{\;}}\left[ {2000\left\{ {{{\left( {1\; + \;\frac{{40}}{{100}}} \right)}^3} - 1} \right\}} \right]{\rm{\;}} = {\rm{\;Rs}}.3488)$
Required CI for 2 years $(= \;\left[ {2000\left\{ {{{\left( {1\; + \;\frac{{40}}{{100}}} \right)}^2} - 1} \right\}} \right]{\rm{\;}} = {\rm{\;Rs}}.1920)$
Interest for the third year = 3488 – 1920 = Rs. 1568
∴ Interest for the third year = Rs. 1568