Question

Future Value At age 30 you invest $2,500 that earns 7.25 percent each year. At age 40 you invest $2,500 that earns 10.25 percent per year. In which case would you have more money at age 60?

Multiple Choice

• At age 40 invest $2,500 at 10.25 percent.

• Both yield the same amount at age 60.

• At age 30 invest $2,500 at 7.25 percent.

• There is not enough information to determine which case earns the most money at age 60.

Answer 1

Ans :

Formula to compute future value of sum invested at a rate of r for n number of years compounded yearly,

FV = PV * (1+r)ⁿ

case (i) FV At age 30 you invest $2,500 that earns 7.25 percent each year

FV = Future value = ?

PV = Present value = $ 2500

r = rate of interest = 7.25 %

n = number of years = 60 -30 = 30

Insert above data in the formula, FV = 2500 * (1+7.25%)³⁰

= 2500 *(1.0725)³⁰

= 2500 * 8.1643013

FV = $ 20,410.75

case (ii) FV At age 40 you invest $2,500 that earns 10.25 percent per year

FV = Future value = ?

PV = Present value = $ 2500

r = rate of interest = 10.25 %

n = number of years = 60 -40 = 20

Insert above data in the formula, FV = 2500 * (1+10.25%)²⁰

= 2500 * (1.1025)²⁰

= 2500 * 7.039988

= $ 17599.97

From above calculation , FV invested at age 30 for 2500 at 7.25% is yielding more value than FV invested at age 40 for 2500 at 10.25%

Option C is correct.