Question

Find the principal amount for the rate of interest 10% p.a. time 3 years and compound interest earned is Rs.993.

Answer 1

Hint: We are given that the number of years is 2 and the rate of interest is 10% and the compound interest obtained is 993. We can find the principal amount by using the formula of compound interest .$C.I = P\left\{ {\left. {{{\left( {1 + \frac{r}{{100}}} \right)}^n} - 1} \right\}} \right.$.

Complete step-by-step answer:
We need to find the principal amount from given details.
We are give that it is compound interest
The formula to calculate compound interest
$ \Rightarrow C.I = P\left\{ {\left. {{{\left( {1 + \frac{r}{{100}}} \right)}^n} - 1} \right\}} \right.$
And here the C.I is the compound interest and n is the number of years and r is the rate of interest and P is the principle amount.
C.I = 993
n = 3
r = 10
$
   \Rightarrow C.I = P\left\{ {\left. {{{\left( {1 + \frac{r}{{100}}} \right)}^n} - 1} \right\}} \right. \\
   \Rightarrow 993 = P\left\{ {\left. {{{\left( {1 + \frac{{10}}{{100}}} \right)}^3} - 1} \right\}} \right. \\
   \Rightarrow 993 = P\left\{ {\left. {{{\left( {1 + 0.1} \right)}^3} - 1} \right\}} \right. \\
   \Rightarrow 993 = P\left\{ {\left. {{{\left( {1.1} \right)}^3} - 1} \right\}} \right. \\
   \Rightarrow 993 = P\left\{ {\left. {1.331 - 1} \right\}} \right. \\
   \Rightarrow 993 = P\left\{ {\left. {0.331} \right\}} \right. \\
   \Rightarrow \frac{{993}}{{0.331}} = P \\
   \Rightarrow P = 3000 \\
$
Now we get that the principal amount is 3000.

Note: Compound interest makes your money grow faster because interest is calculated on the accumulated interest over time as well as on your original principal.
Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from the simple interest where interest is not added to the principal while calculating the interest during the next period. Compound interest finds its usage in most of the transactions in the banking and finance sectors and also in other areas as well. Some of its applications are:
Increase or decrease in population.
The growth of bacteria.
Rise or Depreciation in the value of an item.