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If the rate of simple interest is 12% per annum and compound interest is 10% annually, find the difference in the interest earned after a period of 2 years on a sum of Rs. 1500.
- ARs. 125
- BRs. 75
- CRs. 150
- DRs. 45
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CCommunity
We know that, $(SI = \frac{{P \times R \times \;T}}{{100}})$
Where, SI = Simple interest; P = Principal amount; R = % rate of interest; T = time in years
Here, for simple interest:
Principal = Rs. 1500
Time = 2 years
Rate of Simple Interest = 12%
$(\therefore \;SI = \frac{{P \times R \times \;T}}{{100}} = \frac{{1500 \times 2 \times 12}}{{100}} = 360)$
⇒ Simple interest = Rs. 360
Now, Compound interest = $({\rm{P}}\left\{ {{{\left( {1 + \frac{{\rm{r}}}{{100}}} \right)}^t} - 1} \right\})$
For compound interest:
Principal = Rs. 1500
Time = 2 years
Rate of compound interest = 10% annually
∴ Compound interest = $(1500\left\{ {{{\left( {1 + \frac{{10}}{{100}}} \right)}^2} - 1} \right\})$ = Rs. 315
∴ Difference in the interest = 360 – 315 = Rs. 45
Where, SI = Simple interest; P = Principal amount; R = % rate of interest; T = time in years
Here, for simple interest:
Principal = Rs. 1500
Time = 2 years
Rate of Simple Interest = 12%
$(\therefore \;SI = \frac{{P \times R \times \;T}}{{100}} = \frac{{1500 \times 2 \times 12}}{{100}} = 360)$
⇒ Simple interest = Rs. 360
Now, Compound interest = $({\rm{P}}\left\{ {{{\left( {1 + \frac{{\rm{r}}}{{100}}} \right)}^t} - 1} \right\})$
For compound interest:
Principal = Rs. 1500
Time = 2 years
Rate of compound interest = 10% annually
∴ Compound interest = $(1500\left\{ {{{\left( {1 + \frac{{10}}{{100}}} \right)}^2} - 1} \right\})$ = Rs. 315
∴ Difference in the interest = 360 – 315 = Rs. 45