Another common question that often arises in retirement planning: How much does a client need to invest today over a period of time to accomplish certain financial objectives or future values?

EXAMPLE

Your prospect's goal is to have $10,000 at the end of 5 years. How much principal does shehavetosetasidetodayat7percentinteresttoaccomplishthis?

You can make the calculation by using an inverse variation of the compound interest formula FVSS = I (1 + i)n, where future value of a single sum is found by multiplying a current investment amount by 1 plus a specified interest rate over time, and present value is found by dividing the targeted future value of a single sum by the future value objective ($10,000) by 1 plus a specified interest rate over time:

PVSS = FVSS ÷ (1 + i)n

PVSS = $10,000 ÷ (1 +.07)⁵

PVSS = 10,000 ÷ (1.403) = $7,128

Or the formula can be expressed as

          PVSS = FVSS × [1 ÷ (1 + i)n]

where PVSS = percent value of a single sum

          FVSS = future value of a single sum

                i = compoundannualinterestordiscountrateexpressed as a decimal

               n = numberofyearsoverwhichdiscountingoccurs

1 ÷ (1 + i)n = PVSS factor

Since the term [1÷(1+i)n] in the PVSS formula is the PVSS factor, the PVSS formula can be simplified and written as follows:

PVSS = FVSS x PVSS factor

Thus, you can also make the calculation using the compound discount table titled "One Dollar Principal" in appendix A. The factor for 7 percent for 5 years (.713). In our example this is

PVSS = $10,000 x (.713) = $7,130

Note: The difference between the answers of $2.00 ($7,128 versus $7,130) is due to the rounding of numbers within the two tables.

Thus, your prospect needs to invest $3,719 now and each yeartoaccumulate $100,000 at the end of the 15-year period.

 FA 261 use Table A-3.

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Prudent investors often develop a habit of periodically depositing a set amount of money into a savings account or other investment vehicle. For example, your client may wish to deposit $5,000 per year into an investment at the beginning of each year for 5 years, earning 6 percent interest. This scenario describes a future value of periodic deposits (FVPD) problem. Periodic deposits are a series of equal payments made at the beginning of each year (or period) for a specified number of years (or periods).

The formula to calculate the future value of periodic deposits is as follows:

          FVPD = I (1 + i)n

where FVPD = future value of periodic deposits

                I = amount invested each period

    I (1 + i)n = FVif = futurevalueinterestfactorfor the periodic investment (See table," One Dollar per Annum in Advance," in appendix A.)

EXAMPLE:

Assume that your client begins today to deposit $5,000 each year for the next 3 years at an annual interest rate of 6 percent. How much will he have at the end of 3 years?

The factor from the compound interest table for a 6 percent interest rate and a 3-year investment horizon is 3.375. Thus, the future value of the deposits in this example is

FVPD = $5,000 x 3.375 = $16,875

Logic dictates that the higher the interest rate and the longer the time horizon, the higher the future value will be.

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 FA 261 use Table A-2.

FVSS = I(1+i)ⁿ

FVSS = Future Value of a Single Sum

      I = amount of the initial investment

      i = annual interest rate

     n = number of years or compounding periods of the investment

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FA 261 use Table A-2.