At the end of 10 years, which of the following investments would have the highest future value?Assume that the effective annual rate for all investments is the same and is greater than zero.
A) investment a pays $250 at the beginning of every year for the next 10 years (a total of 10 payments).
B) investment b pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments).
C) investment c pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments).
D) investment d pays $2,500 at the end of 10 years (just one payment).
E) investment e pays $250 at the end of every year for the next 10 years (a total of 10 payments).

Question

Quizplus · Accepted Answer

A dominates B because it provides the same total amount, but it comes faster, hence it can earn more interest over the 10 years. A also dominates C and E for the same reason, and it dominates D because with D no interest whatever is earned. We could also do these calculations to answer the question:
 $\begin{array} { c c c c c c r } 
\mathrm { A } & \$ 4,382.79 & \text { Largest } & \text { EFF\% } & 10.00 \% & 10 & 250 \
\mathrm {~B} & \$ 4,081.59 & & \mathrm { NOM } \% & \mathbf { 9 . 7 6 \% } & &125 \
\mathrm { C } & \$ 4,280.81 & & & && 125 \
\mathrm { D } & \$ 2,500.00 & & & && 2500 \
\mathrm { E } & \$ 3,984.36 & & & && 250
\end{array}$

At the End of 10 Years, Which of the Following