Question

Find the amount on RS12500 for 2 years compounded annually, the rate of interest being 15% for the first year and 16% for the second year.
A). Rs16500
B). Rs16750
C). Rs16675
D). None of these

Answer 1

Hint: Here, we will first calculate the amount for first year on 15% rate of interest. Then, the amount obtained will be the principal for the second year. Now, we will calculate the amount on this principal for the second year at a 16% rate of interest. The formula used for calculating amount is
$ \Rightarrow A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}$

Complete step-by-step solution:
In this question, we are given an amount and we need to find the interest on it given that the rate of interest for the first year is 15% and 16% for the second year.
Given data:
Principle$ = Rs12500$
Rate for 1st year ${R_1} = 15\% $
Rate for 2nd year ${R_2} = 16\% $
Amount$ = ?$
Now, first of all let us calculate the amount for principle Rs12500 for 1 year at rate of interest being 15%.
Now, we know the formula that
$ \Rightarrow A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}$
Where, $P = $Principle, $r = $ rate of interest and $n = $ time period.
So, here we have $P = 12500$, $r = 15\% $ and $n = 1$. Here the time period is only one year as we are finding the amount for only one year. Therefore,
$
   \Rightarrow A = 12500{\left( {1 + \dfrac{{15}}{{100}}} \right)^1} \\
   \Rightarrow A = 12500\left( {\dfrac{{100 + 15}}{{100}}} \right) \\
   \Rightarrow A = 12500\left( {\dfrac{{115}}{{100}}} \right) \\
   \Rightarrow A = 12500\left( {1.15} \right) \\
   \Rightarrow A = Rs14375 \\
 $
Hence, we get an amount of Rs14375 after one year at a rate of interest of 15%. Now, we need to find the amount for the second year.
For the second year, our principal will be Rs14375 and rate of interest is given as 16%. Therefore,
$
   \Rightarrow A = 14375{\left( {1 + \dfrac{{16}}{{100}}} \right)^1} \\
   \Rightarrow A = 14375\left( {\dfrac{{100 + 16}}{{100}}} \right) \\
   \Rightarrow A = 14375\left( {\dfrac{{116}}{{100}}} \right) \\
   \Rightarrow A = 14375\left( {1.16} \right) \\
   \Rightarrow A = Rs16675 \\
 $
Hence, after two years the amount will be Rs16675.
Hence, our answer is option C.

Note: The most important part in this question is that we have to take the principal amount for the second year as the amount we obtained after the first year. If this seems a little confusing, there is a direct formula also that can be used.
$
   \Rightarrow A = P\left( {1 + \dfrac{{{r_1}}}{{100}}} \right)\left( {1 + \dfrac{{{r_2}}}{{100}}} \right) \\
   \Rightarrow A = 12500\left( {1 + \dfrac{{15}}{{100}}} \right)\left( {1 + \dfrac{{16}}{{100}}} \right) \\
   \Rightarrow A = 12500\left( {1.15} \right)\left( {1.16} \right) \\
   \Rightarrow A = Rs16675 \\
 $