Question: Quing deposits $40 at the end of each month into a savings account. If the money earns 4% annum compounded monthly, how much money is in the account at the end of 24 months?

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Calculate the present value of an annuity, if $150 payments are to be made monthly for 4 years and the interest rate is 9% per annum compounded monthly.

Hi Kerem,

When solving compound interest questions, we need to know the formula for compound interest and what the variables mean, so that we can substitute values.

This is the formula:

T = P(1 + i)ⁿ , where T is the total amount in the account after n compounding periods.  P is the principle amount (the amount you start with) and i is the rate of interest for 1 compounding period.

For example, let’s say we deposit $1000 into a saving account that earns 4% interest each year, compounded quarterly.  How much money will we have at the end of 10 years?

T = P(1 + i)ⁿ
T = 1000(1 + 0.01)⁴⁰
T = $1488.86

In this problem, n is 40 because the interest is compounded four times a year (quarterly) for ten years.  The interest rate is set at 1% because our money earns 1% interest each time the interest is compounded. 

Try substituting your specific values for your question into this formula.  Remember, you might not always be solving for T, so you may need to manipulate the formula to find what you’re looking for. You may need also to use the expression more than once to solve a problem. For example for your first problem

• Quing has $40 in his account at the end of the first month.
• At the end of the second month he has $40 more that he deposits plus the result of applying the expression above with P the amount in his account at the end of the first month, n = 1 and i the rate of interest for 1 compounding period
• At the end of the third month he has $40 more that he deposits plus the result of applying the expression above with P the amount in his account at the end of the second month, n = 1 and i the rate of interest for 1 compounding period
• ...

Natasha and Penny