Question

Harsha borrows \[Rs.5000\] to purchase a sewing machine from ‘Women Savings Bank’ at $5\% $ rate of compound interest. So at the end of $3$ years how much will she pay?

Answer 1

Hint: There is an equation to find the amount to be paid at compound interest using the rate of interest and term of the loan. Here these data are all given. So we can find the answer by direct substitution.

Useful formula:
If we borrow a principal $P$ at the rate of compound interest $r\% $, then the amount to be paid after $n$ years is,
$ \Rightarrow A = P{(1 + \dfrac{r}{{100}})^n}$

Complete step by step solution:
Given that Harsha borrows $Rs.5000$ at the rate of $5\% $ compound interest.
We have to find the amount of money she has to be paid after three years.

This amount includes the principal borrowed and the interest for the three years.
If we borrow a principal $P$ at the rate of compound interest $r\% $, then the amount to be paid after $n$ years is,
$ \Rightarrow A = P{(1 + \dfrac{r}{{100}})^n}$
Here, $P = 5000,r = 5,n = 3$
Substituting these values in the equation we get,
$A = 5000{(1 + \dfrac{5}{{100}})^3}$
Simplifying the above equation we get,
$A = 5000{(1 + \dfrac{5}{{100}})^3} = 5000 \times {(\dfrac{{105}}{{100}})^3}$
Expanding the cube power we get,
$A = 5000{(\dfrac{{105}}{{100}})^3} = 5000 \times \dfrac{{105 \times 105 \times 105}}{{100 \times 100 \times 100}}$
Cancelling $5$ from $105,100$ we get,
$A = 5000 \times \dfrac{{21 \times 21 \times 21}}{{20 \times 20 \times 20}} = 5000 \times \dfrac{{21 \times 21 \times 21}}{{8000}} = \dfrac{5}{8} \times 9261 = 5788.125$

Therefore the amount to be paid is $Rs.5788.125$ which is approximately equal to $Rs.5788$.

Additional information:The compound interest need not be calculated annually. If it is not, then there is a difference in the formula.
In those cases, the amount, $A = P{(1 + \dfrac{r}{n})^{nt}}$, where $P,r,n,t$ represent the principal, rate of interest, number of times interest is compounded per time period, number of time periods respectively.

Note: Here we are asked to find the amount to be paid. Sometimes we may ask to find the interest. In those cases, calculate the amount using this formula. Then subtract the principal from the amount and hence we get the interest. Also be careful about whether the interest is calculated annually or not and use appropriate formulas.