3: The Time Value of MoneyEquation 3.5 demonstrates that the future value of an annuity due always exceeds the future value
of a similar ordinary annuity (for any positive interest rate) by a factor of 1 plus the interest rate. We can
check this by comparing the results from the two different five-year vacation savings plans presented
earlier. We determined that, given a 7% interest rate, after five years the value of the ordinary annuity
was $5,750.74, and that of the annuity due was $6,153.29. Multiplying the future value of the ordinary
annuity by 1 plus the interest rate yields the future value of the annuity due:
FV (annuity due) = $5,750.74 × (1.07) = $6,153.29
FIGURE 3.9 FUTURE VALUE AT THE END OF FIVE YEARS OF AN ANNUITY DUE OF $1,000 PER YEAR INVESTED AT 7%The future value at the end of five years of a five-year, $1,000 annuity due that earns 7% annual interest is $6,153.29,
which exceeds the $5,750.74 future value of the otherwise identical ordinary annuity (see Figure 3.8). Each deposit in the
annuity due earns one more year of interest than the comparable deposit into the ordinary annuity.
Formula B4: =FV(B3,B2,B1,0,1)Future value $6,153.29Interest rate 7%5
–$1,000
Number of periodsPaymentInputNote: switch calculator to BEGIN mode.Note: switch calculator to END mode.Solution–1,000
5
7
PMT
N
I
CPT
FV
6,153.29
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