For how many years would simple interest and compound interest on a sum of money is same

Simple Interest and Compound Interest are different forms of interest, usually either paid by a bank to someone saving money or paid by the borrower of a loan such as a mortgage.

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Is simple interest and compound interest same for 1 year?
How many years will the simple interest on a sum of money be equal to the principle at rate of 12% pa?
On what sum of money will the difference between the compound interest and simple interest?
On what sum of money will the difference between SI and CI for 2 years?

This video and text below show you how to calculate simple and compound interest.

Simple Interest

With simple interest the amount of interest is fixed over a period of time. For example if you were to save £200 at 3% simple interest you would earn £6 per year, every year.

It’s important to note with simple interest the amount earned will stay the same every year.

Compound Interest

Compound interest is the type of interest that is more normally paid out by banks to savers. With compound interest, the interest earned over time will continue to increase as long as no money is withdrawn from the account. This is because all previously earnt interest remains in the account so the sum from which to calculate interest becomes larger over time.

Using the same figures as the simple interest example above (£200 at 3% interest), in year one you would still earn £6. In year two you would continue to earn 3% on the new amount £206 so the interest earnt would be £6.18, taking the total amount to £212.18.

Calculating Simple Interest

If you deposit £250 in a bank account which is paying 5% interest per year. How much simple interest will be earnt over 5 years?

To answer this question you begin by working out 5% of £250 which = £12.50. To calculate the amount of simple interest over 5 years you simply multiply the interest earnt in year one by five - £12.5 × 5 = £62.5.

Calculating Compound Interest

If you deposit £1,000 in a bank account which is paying 3% compound interest per year. How much interest would be earnt over 3 years?

You can handle this question in either of these ways:

Firstly by calculating the amount of interest earnt each year and adding up all the amounts.

Year one – 1000 × 0.03 = 30

Year two – (1000 + 30) x 0.03 = 30.90

Year three – (1030 + 30.90) x 0.03 = 31.83

Total = 30 + 30.90 + 31.83 = 92.73

Secondly you can use a multiplier

Year 3 = 1000 x 1.033 = 1,092.73

1,092.73 – 1000 = £92.73

Solution: Each period is one month long, so the length of time for one period is 1/12 of a year. The interest earned for one period will be I = P × r × ( 1/12). This is the same as we found in Example 1.

In general, if there are m periods in a year, the length of time for each period will be (1/m) of a year. The interest earned in one period will be I = P(r/m).

The periodic interest rate, then, is r/m. We can let I be the periodic interest amount and i = r/m. So the interest earned in one period Is I = Pi. That means the amount of money in an interest-earning account at the end of a period is P + Pi. This looks just like the simple interest formula except the interest rate r is replaced by the periodic interest rate i = r/m.

If an account earns interest compounded every six months, the periodic interest rate per each six-month period is i = 12%/2 = 6%. If the account earns interest compounded quarterly, or four times a year, the periodic interest rate is i = 12%/4 = 3%. Many accounts earn interest each month, so i = r/12.