421.2
2.Let's say you resolve to drink one less beer per month for the
next 40 years. Assume that this represents a savings of $3 per
month. If you take that extra $3 and invest it each month in your
retirement account, how much extra will you have when you retire
in 40 years? Assume your retirement account earns 12% per year,
compounded monthly.
This is a future value of an annuity question:
0 1 2 3 4 ... 480 3 3 3 3 3 PV FV You can calculate the PV of the annuity and then calculate the FV of that PV:
\( \Large PV = P3 \left [ \frac{1}{r} - \frac{1}{r \left(1+r \right )^{n} } \right ] \)
Substituting:
\( \Large PV = 3 \left [ \frac{1}{\frac{.12}{12}} - \frac{1}{\frac{.12}{12} \left(1+\frac{.12}{12} \right )^{480} } \right ] = 3[99.157] = 297.47 \).
This is the PV. You want the FV.
\(\Large 297.47 \left ( 1+ \frac{.12}{12} \right)^{480} \) = $35,294.14