How do you calculate the future value of a lump sum given the present value, interest rate, and time period?

Conditions

• The interest rate r is assumed to remain constant over the period.
• The compounding frequency matches the time unit of n (e.g., annual rate with years).
• The formula assumes a single lump-sum payment rather than an annuity.

Reasoning, step by step

1. Identify the present value (PV), the interest rate (r), and the number of periods (n).
2. Write down the future value formula: $FV = PV(1+r)^n$.
3. Convert the percentage interest rate into a decimal (e.g., 6% becomes 0.06).
4. Substitute the values into the formula: $FV = 10,000(1+0.06)^{20}$.
5. Simplify the term inside the parentheses: $1 + 0.06 = 1.06$.
6. Calculate the exponential part: $(1.06)^{20}$.
7. Multiply the result by the present value to find the final future value.

Example

For a present value of $10,000, an annual interest rate of 6$FV = 10,$000(1.06)^{20}$$, which yields approximately$32,071.35.

Common misconceptions

• Assuming simple interest is used instead of compound interest.
• Forgetting to convert the percentage interest rate to a decimal before calculating.
• Using the wrong number of periods if the compounding frequency differs from the rate's time unit.

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