Question

Find the amount and compound interest on Rs. 4000 in 2 years if the rate of interest for the first year is 10% and for the second year is 15%.

Answer 1

Hint: Given is the principal amount. Generally the rate is not changed but here the rate for the first year and second year is different. So we will use the rates differently.
Formula used:
Amount is given by \[p\left[ {1 + \dfrac{R}{{100}}} \right]\]
Compound interest is given by \[amount - principle\].

Complete step-by-step answer:
Given that the principal amount is P=Rs. 4000
The rate for the first year is 10% and for the second year is 15%.
Now the amount is given by,
\[Amount = p\left[ {1 + \dfrac{{{R_1}}}{{100}}} \right]\left[ {1 + \dfrac{{{R_2}}}{{100}}} \right]\]
Now we will put the values,
\[Amount = 4000\left[ {1 + \dfrac{{10}}{{100}}} \right]\left[ {1 + \dfrac{{15}}{{100}}} \right]\]
On dividing the ratios we get,
\[Amount = 4000\left[ {\dfrac{{11}}{{10}}} \right]\left[ {\dfrac{{23}}{{20}}} \right]\]
\[Amount = 4000 \times \dfrac{{11 \times 23}}{{200}}\]
Now dividing the numbers we get,
\[Amount = 20 \times 11 \times 23\]
On multiplying we get,
\[Amount = 5060\]
This is the amount so obtained but we need to find the compound interest. So we will subtract the principle value from the amount so obtained.
\[C.I. = amount - principle\]
\[C.I. = 5060 - 4000\]
Thus the compound interest is,
\[C.I. = 1060\]
This is the interest so obtained.
So, the correct answer is “\[C.I. = 1060\]”.

Note: Note that the interest in the first year is the same as simple interest. And the compound interest is the interest so obtained on the interest in the first year. Thus always the C.I. is higher than S.I.
We can also find the C.I. directly finding the simple interest formula for first year and the same for second year but in second year the interest is calculated on the interest in first year also.