Question

find the sum of money that amounts to 31740 in 2 years if the interest is compounded annually at the rate of 15% per annum​

Answer 1

Answer:

principal P= Rs.24000

Step-by-step explanation:

Answer 2

The sum of money that amounts to 31740 in 2 years is Rs 24000

Solution:

Given that,

Total amount = 31740

Number of years = 2

Rate of Interest = 15 %

Principal sum = ?

The formula for Total amount when compounded annually is:

$A=P\left(1+\frac{R}{100}\right)^{T}$

Where,

A is the total amount

P is the principal sum

R is the rate of interest

T is the number of years

Plugging in values, we get

$31,740=\mathrm{P}\left(1+\frac{15}{100}\right)^{2}$

$31,740=\mathrm{P}\left(1+\frac{3}{20}\right)^{2}$

On solving we get,

$31,740=\mathrm{P}\left(\frac{23}{20}\right)^{2}$

$\begin{array}{l}{P=\frac{31,740 \times 20 \times 20}{23 \times 23}} \\\\ {P=24000}\end{array}$

Hence the sum of money is Rs 24000

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