Question
Find the difference between Compound Interest and Simple Interest on $Rs. 45,000$ at $12\%$ per annum for $5$ years.
✓
Answer
Principal $(P) = Rs. 45000$
Rate of interest $(R)= 12\%$ per annum
Time period $(T) = 5$ yr
Simple interest ,$\text{SI}=\frac{\text{P}\times\text{R}\times\text{T}}{100}=\frac{45000\times12\times5}{100}$
$=450\times60=\text{Rs}. \ 27000$
Compound interest, $CI = A - P$ Where, $\text{A}=\text{P}\Big(1+\frac{\text{R}}{100}\Big)^\text{T}$$\text{A}=45000\Big(1+\frac{\text{12}}{100}\Big)^\text{5}=45000\Big(\frac{28}{25}\Big)^5$
$=45000\times\frac{28}{25}\times\frac{28}{25}\times\frac{28}{25}\times\frac{28}{25}\times\frac{28}{25}$
$=\frac{45000\times17210368}{9765625}=45000\times1.76$
Compound interest , $\text{CI}=\text{Rs.}79200$$-\text{Rs}. \ 45000=\text{Rs.} \ 34200$
Difference between $\text{SI} \ \text{and} \ \text{CI}=\text{Rs.} \ 34200$$-\text{Rs}. \ 27000=\text{Rs.} \ 72000$
Rate of interest $(R)= 12\%$ per annum
Time period $(T) = 5$ yr
Simple interest ,$\text{SI}=\frac{\text{P}\times\text{R}\times\text{T}}{100}=\frac{45000\times12\times5}{100}$
$=450\times60=\text{Rs}. \ 27000$
Compound interest, $CI = A - P$ Where, $\text{A}=\text{P}\Big(1+\frac{\text{R}}{100}\Big)^\text{T}$$\text{A}=45000\Big(1+\frac{\text{12}}{100}\Big)^\text{5}=45000\Big(\frac{28}{25}\Big)^5$
$=45000\times\frac{28}{25}\times\frac{28}{25}\times\frac{28}{25}\times\frac{28}{25}\times\frac{28}{25}$
$=\frac{45000\times17210368}{9765625}=45000\times1.76$
Compound interest , $\text{CI}=\text{Rs.}79200$$-\text{Rs}. \ 45000=\text{Rs.} \ 34200$
Difference between $\text{SI} \ \text{and} \ \text{CI}=\text{Rs.} \ 34200$$-\text{Rs}. \ 27000=\text{Rs.} \ 72000$
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