Question

What is the compound interest on Rs.5000 for 3 years at 8% for the first year, 10% for the second year and 12% for the third year?

Answer 1

Hint – In order to find the total amount of compound interest calculated over a span of 3 years, we take in the data given in the question and apply the formula of compound interest for first year, second year and third year individually and add all of them to find total interest.

Complete step-by-step answer:
Given Data,
Principle P = 5000/-
Rate of interest in first year = 8%
Rate of interest in second year = 10%
Rate of interest in third year = 12%

Compound interest is when the interest obtained on the principle amount is added to the principle before calculating the interest for the next time period.
It is basically simple interest, which is added to the principle after every time period after which interest is calculated.

In our question the simple interest calculated after the first year is added to the principal amount and then the interest for the second year is calculated and so on.
Simple interest is calculated by the formula, ${\text{Interest = }}\dfrac{{{\text{PRT}}}}{{100}}$, where P is the principle, R is the rate of interest and T is the time period respectively.

Now for the first year,
P = 5000 and R = 8%
${\text{Interest = }}\dfrac{{5000 \times 8 \times 1}}{{100}} = 400{\text{ Rs}}$
Total Amount after first year = P + I = 5000 + 400 = Rs 5400


Now for the second year principle becomes the total amount after the first year,
P = 5400 and R = 10%
${\text{Interest = }}\dfrac{{5400 \times 10 \times 1}}{{100}} = 540{\text{ Rs}}$
Total Amount after second year = P + I = 5400 + 540 = Rs 5940

Now for the third year principle becomes the total amount after the second year,
P = 5940 and R = 12%
${\text{Interest = }}\dfrac{{5940 \times 12 \times 1}}{{100}} = 712.8{\text{ Rs}}$
Total Amount after second year = P + I = 5940 + 712.8 = Rs 6652.8

Therefore the total compound interest after a span of 3 years is given by,
Compound Interest = Total amount after 3 years – Initial Principal amount
C.I = 6652.8 – 5000
C.I = 1652.8 Rs

The total compound interest after a span of 3 years is 1652.8 rupees.

Note – In order to solve this type of question the key is to know the definition and how compound interest works. Knowing that the principal value is changed for every time period (1 year in this question) is an important step in this question.
Compound interest is what happens in our day to day life while taking loans etc.
We could also solve this problem by directly applying a formula which is derived from the original compound interest formula, i.e.
${\text{C}}{\text{.I = P}}\left[ {\left( {1 + \dfrac{{{{\text{R}}_1}}}{{100}}} \right)\left( {1 + \dfrac{{{{\text{R}}_2}}}{{100}}} \right)\left( {1 + \dfrac{{{{\text{R}}_3}}}{{100}}} \right) - 1} \right]$, where ${{\text{R}}_1},{{\text{R}}_2},{{\text{R}}_3}$are the rates of interest in the first, second and the third years respectively.