Of the following investments, which would have the lowest present 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 end 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 beginning of every year for the next 10 years (a total of 10 payments).

Question

Quizplus · Accepted Answer

A is smaller than E and B is smaller than C because the money comes in later. A is smaller than B because a larger annuity is received later. So, now the choice comes down to either A or D. Since all of D is received at the end, this is the logical choice. We could also do these calculations to answer the question:
 $\begin{array} { c c c c c c r } 
\mathrm { A } & \$ 1,536.14 & & \text { EFF\% } & 10.00 \% & 10 & 250 \
\mathrm {~B} & \$ 1,573.63 & & \mathrm { NOM } \% & \mathbf { 9 . 7 6 \% } & &125 \
\mathrm { C } & \$ 1,650.44 & & & && 125 \
\mathrm { D } & \$963.86  &\text { Smallest } & & && 2500 \
\mathrm { E } & \$1.689 .76& & & && 250
\end{array}$

Of the Following Investments, Which Would Have the Lowest Present