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Before we begin, it's useful to review how compound interest is defined. Unlike simple interest, which is only paid on the principal, compound interest is paid on both the principal and the previously accrued interest. The compounding interval is the number of times per year that compound interest is calculated and applied.
First, use pencil and paper, a calculator, or a spreadsheet to answer the following question: If $2,000 is deposited at 3% interest, what will be the value of a savings account each year for 4 years, assuming no withdrawals or deposits and an annual compounding of interest? Remember, compound interested is paid on both the principal and the accrued interest.
| End of Year |
Account Value |
| 0 |
$2000 |
| 1 |
$? |
| 2 |
$? |
| 3 |
$? |
| 4 |
$? |
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After you have worked on the problem, select "Show Answer" to see our response.
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Show Answer |
Sample Answer:
For the first year, the total value is the principal + interest, or $2,000 + (.03 • $2,000) = $2,060. To find the total value for the second year, we add the interest, .03, to the first-year total. The equation might look like this: $2,000 + (.03 • $2,000) + .03($2,000 + [.03 • $2,000])
This gives us $2,121.80. If we follow the same procedure for the remaining years, we would get the results above:
Do you see how the values were determined?
This solution method provides an answer for each year, but it quickly becomes tedious.
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 Simplifying the calculation
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