Question

Jarom and Christina are twins. Both Jarom and Christina invest $5,000 each year beginning when they are 30 years old. Jarom's investment pays 7 percent annually with semi-annual compounding, while Christina's pays 7 percent annually with monthly compounding. Both Jarom and Christina retire at age 70. Which one of the following statements is correct?

Christina will have the same amount as Jarom when they retire.
Jarom will earn more in interest than Christina.
Christina will have more than Jarom when they retire.
Christina and Jarom earn the same amount of interest each year.
Christina will have less than Jarom when they retire.

Answer 1

Christina will have more than Jarom when the retire

Step-by-step explanation:

The total amount earned after a given number of years can be expressed as;

A=P(1+r/n)^nt

where;

A=total amount earned

P=initial investment

r=annual interest

n=number of compounding periods in a year

t=number of years

Consider Jarom's;

P=$5,000

r=7%=7/100=0.07

n=2

t=(70-30)=40 years

replacing;

A=5,000(1+0.07/2)^(2×40)

A=5,000(1.035)^80

A=$78,378.6877

Jarom will have a total of $78,378.6877 by retirement

Consider Christina's total amount;

P=$5,000

r=7%=7/100=0.07

n=12

t=40

replacing;

A=5,000(1+0.07/12)^(12×40)

A=$81,557.057

Christina will have a total of $81,557.057 by retirement

Christina will have more than Jarom when the retire