Question

You want to create a fund so that you can attend an Alabama Bowl Game every year for the next 30 years. You estimate that you will need $5000 each year. If you invest $6000 the first year and increase the investment by $500/yr, all at 4% interest, how many years do you have to invest to meet your goal?

Answer 1

ANSWER:

I = 4%

N = 30 YEARS

We will find the present worth of the money for $5,000 per year.

pw = amount per year(p/a,i,n) = 5,000(p/a,4%,30) = 5,000 * 17.292 = 86,460

now we will find the no of years required to fulfill this amount and the pw for the number of years should be more or equal to the present worth.

pw = investment in1st year(p/a,i,n) + increase in investment per year(p/g,i,n)

86,460 = 6,000(p/a,4%,n) + 500(p/g,4%,n)

solving via trial and error by looking into compounding factor tables for i = 4% that the present value for n at 12 years is 79,934 while at n at 13 years is 87,143.5 and so the value of n is between 12 and 13 years and so he would have invested for at least 13 years to get the amount of funds required for the game for the next 30 years.

n = 13