Question

On January 1, Alan King decided to transfer an amount from his checking account into an investment account that later will provide $80,000 to send his son to college (four years from now). The investment account will earn 8 percent, which will be added to the fund each year-end. (Future Value of $1, Present Value of $1, Future Value Annuity of $1, Present Value Annuity of $1) (Use appropriate factor(s) from the tables provided.)

Answer 1

Answer:

The requirement of the question is as below:

How much must Alan deposit on January 1? (Round your final answer to the nearest whole dollar amount.)  

What is the interest for the four years? (Round your final answer to the nearest whole dollar amount.)

Alan deposit on January 1 is $ 58,802.39  

Interest for four years is $21,197.61

Explanation:

The first is asking for today's worth of the investment,which is the amount to be invested,this can be computed using the present value as shown below:

PV=FV*(1+r)^-n

PV is the present value

FV is the worth of the investment in 4 years from now which is $80,000

r is the rate of return of 8%

n is the number of years of investment which is 4 years

PV=$80,000*(1+8%)^-4

PV=$80,0008(1+0.08)^-4

PV=$80,000*(1.08)^-4

PV =$ 58,802.39  

interest for four years=FV-PV

interest for four years=$80,000-$ 58,802.39  

                                    =$21,197.61