What is difference simple interest and compound interest on rupees 1000 for 4 years at 20% per annum(componded yearly)
Answers
Step-by-step explanation:
The difference between ‘simple’ and compound interest is that the first only accumulates interest on the principal amount and the latter also accumulates interest on the interest itself. In other words: the interest is ‘re-invested’ and becomes interest bearing as well.
The difference will be Rs 1,400 - Rs 1,464.10 = Rs 464.10
To give the calculation for both methods:
(1) ‘simple’ interest:
Rs 1,000 * (100%+10%) * 4 years = Rs 1,400
after one year: Rs 1,000 + 1 * [Rs 1,000 * 10%] = Rs 1,100
after two years: Rs 1,000 + 2 * [Rs 1,000 * 10%] = Rs 1,200
after three years: Rs 1,000 + 3 * [Rs 1,000 * 10%] = Rs 1,300
after four years: Rs 1,000 + 4 * [Rs 1,000 * 10%] = Rs 1,400
(2) compound interest:
Rs 1,000 * (100% + 10%) * (100% + 10%) * (100% + 10%) * (100% + 10%)
= Rs 1,000 * (100% + 10%)^4
= Rs 1,464.10
after one year: Rs 1,000 * (100%+10%) = Rs 1,100
after two years: Rs 1,100 * (100% + 10%) = Rs 1,210
after three years: Rs 1,210 * (100% + 10%) = Rs 1,331
after four years: Rs 1,331 * (100% + 10%) = Rs 1,464,10
Please, take a closer look at the difference in the total of both methods after 2 years. You will notice that the difference = Rs 1,200 - Rs 1,210 = Rs 10
This difference is caused by the fact that in the compound method , next to the interest on the principal amount, the interest is also calculated on the interest of year 1: Rs 100 * 10% = Rs 10 Q.E.D.