Question

Sixteen years ago, Alicia invested $500. Eight years ago, Travis invested $900. Today, both Alicia's and Travis' investments are each worth $2,400. Assume that both Alicia and Travis continue to earn their respective rates of return. Which one of the following statements is correct concerning these investments?
a. Three years from today, Travis' investment will be equal to Alicia's
b. One year ago, Alicia's investment was worth same as Travis' investment.
c. Travis earns a higher rate of return than Alicia.
d. Travis has earned an average annual interest rate of 3.37 percent.
e. Alicia has earned an average annual interest rate of 6.01 percent.

Answer 1

Answer:

c. Travis earns a higher rate of return than Alicia.

Explanation:

Both investments are worth $2,400.

Alicia's rate of of return is given by:

$FV=PV(1+r)^n\\2,400=500*(1+r)^{16}\\1+r=\sqrt[16]{4.8}\\r=0.103$

Travis' rate of return is given by:

$FV=PV(1+r)^n\\2,400=900*(1+r)^{8}\\1+r=\sqrt[8]{2.66667}\\r=0.130$

Alicia's investment had a rate of return of roughly 10.3% while Travis' investment had a rate of return of about 13.0%.

Therefore, the we can conclude that c. Travis earns a higher rate of return than Alicia.