Question

The simple interest on 15000 for a time period at 8% per annum is 2400. What will be the compound interest on the same sum at the same rate for that time period?

Answer 1

$\underline{\underline{\maltese\: \: \textbf{\textsf{Question}}}}$

The simple interest on 15000 for a time period at 8% per annum is 2400. What will be the compound interest on the same sum at the same rate for that time period?

$\underline{\underline{\maltese\: \: \textbf{\textsf{Answer}}}}$

$\sf\small\underline\red{Given:-}$

Simple interest =₹ 2400

Interest rate =8% per annum

Time =2 years

$\sf\small{We \: know \: that \: simple \: interest (SI)= \frac{PTR}{100} }$

where P is principle amount, T is time taken, R is rate per annum

So,

$\sf\small{2400=(P×2×8)/100}$

$\sf\small{On \: rearranging \: we \: get,}$

$\sf\small\{P=2400×25 = ₹15000 }$

$\sf\small{Hence, \: the \: sum \: is \: ₹ \: 15000}$

$\sf\small\underline\red{To \: find:-}$

the amount we have the formula,

Amount (A)=P(1+(r/100))n

where P is present value, r is rate of interest, n is time in years.

Now substituting the values in above formula we get,

$\sf\small{∴A=15000(1+8/100)²}$

$\sf\small{⟹ A=15000(108/100)²}$

$\sf\small{⟹ A=600(27/25)²}$

$\sf\small{⟹ A=24(27)(27)}$

$\sf\small{⟹ A=₹ 17496}$

$\sf\small \red{And \: Compound \: interest =A - P}$

$\sf\small{=17496–1500 =₹ 2496}$