Question

Ramlal deposits 30000 rupees in a financial establishment which pays interest at 9% annual rate, compounded every four months. How much would he get back after one year?

Answer 1

Hint: We have to find how many times interest is calculated in one year. And after that we can apply compound interest formula i.e. \[A = P{\left( {1 + \dfrac{r}{{100 \times n}}} \right)^{nt}}\] directly to get the amount Ramlal has after one year.

Complete step-by-step answer:
As we know that the principal amount is Rs. 30000.
Rate of interest is 9% at annual rate.
And rate of interest is compounded every four months.
So, one year has 12 months.
Hence, no of times the interest compounded in one year will be \[\dfrac{{12}}{4} = 3\]
So, now we can apply compound interest formulas to find the amount after one year.
According to compound interest formula compound interest for t years is calculated as \[A = P{\left( {1 + \dfrac{r}{{100 \times n}}} \right)^{nt}}\]where r is the annual rate of interest, n is the number of times compounded in one year, and t will be number of years after which we had to find the amount, P will be the principal amount and A will be the amount after t years.
So, according to the question,
P = Rs. 30000
r = 9%
n = 3
and t = 1years.
So, putting all the values in the formula of compound interest we will get,
\[A = 30000{\left( {1 + \dfrac{9}{{3 \times 100}}} \right)^{3 \times 1}} = 30000{\left( {\dfrac{{309}}{{300}}} \right)^3} = 30000{\left( {\dfrac{{103}}{{100}}} \right)^3}\]
So, \[A = 30000 \times \dfrac{{103}}{{100}} \times \dfrac{{103}}{{100}} \times \dfrac{{103}}{{100}} = \dfrac{{3 \times 103 \times 103 \times 103}}{{100}} = 32781.81\]
Hence, the amount Ramlal have after one year will be equal to Rs. 32781.81

Note: Whenever we come up with this type of question then to apply compound interest formula first we have to find the value of n which is equal to the number of times interest is compounded annually and to find that we can divide number of months after which interest is compounded with 12 (1 year = 12 months). And after that we can put all the value in the equation \[A = P{\left( {1 + \dfrac{r}{{100 \times n}}} \right)^{nt}}\] to get the value of A which will be the amount Ramlal have after one year.