Time value of money problems ask how cash changes in value over time. A present value question moves a future amount back to today; a future value question moves money today forward. The calculations become easier when you first identify what you know and what you need to find. Then match the interest rate and number of periods to the same time unit, choose the appropriate formula, and check whether your answer makes sense.
Sort the Given Information
Start by listing the values in the problem: present value (PV), future value (FV), interest rate per period (r), and number of periods (n). Mark the unknown. If the problem describes regular deposits or withdrawals, note the payment amount (PMT) and whether each payment happens at the beginning or end of a period.
Draw a simple timeline if the wording feels confusing. Label today as time zero, then mark each year, month, or other period. Place each cash flow where it occurs. This helps distinguish a single lump sum from a series of payments and shows whether you are moving money forward or backward in time.
Match Rates and Periods
The rate and period count must use the same unit. For annual compounding over five years, use the annual rate and five periods. For monthly compounding over five years, convert the annual rate to a monthly rate as directed by the problem and count 60 monthly periods. Do not combine a monthly rate with a five-year period count.
Read carefully to determine whether the stated rate is annual or already given per period, and whether interest compounds annually, monthly, or on another schedule. Keep percentage and decimal forms straight: enter 6% as 0.06 in a formula. Follow the specific compounding convention provided rather than assuming one.
Calculate Present or Future Value
For a single amount, future value is FV = PV × (1 + r)^n. Use it when you know the amount today and want its value after n periods. For example, if $1,000 earns 5% per year for three years, calculate $1,000 × (1.05)^3. Keep the full value in your calculator and round only the final result.
To find present value, reverse the process: PV = FV ÷ (1 + r)^n. Use this when you know a future amount and need its value today at the stated rate. Enter the future amount, rate, and period count carefully, including parentheses around the growth factor before raising it to a power.
Check the Result
Ask whether the direction of the answer makes sense. With a positive interest rate, a single amount’s future value should be greater than its present value, while its present value should be less than the future amount. If your result goes the other way, check for a sign error, a misplaced exponent, or a mismatch between the rate and periods.
Use a financial calculator or spreadsheet as a second check, but enter the timing and payment settings deliberately. For annuities, confirm whether payments occur at the beginning or end of each period. If you are practicing with Coastal Math Tutoring, bring the original wording and your setup so you can pinpoint which step needs attention.
A dependable approach is to identify the unknown, map the cash flows, align the rate with the period count, and apply the matching formula. Write down each step before using a calculator so errors are easier to spot. With practice, these problems become more systematic; consider working through a few examples with a tutor if you want guided feedback.