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g Jill has a balance of $866,000 in her retirement savings account. She expects to retire in 8 years. She will not save any additional money until she retires, but what she has in savings now will earn 9% for the next 8 years. Bob has a balance of $482,000 in his retirement savings and he also wants to retire 8 years from now. He plans to save money every year for the next 8 years so that he will have exactly as much money as Jill does 8 years from now. If he earns the same rate on his savings as Jill, how much will he have to save each year for 8 years to catch up with Jill

Sagot :

Answer:

$69,378.96

Explanation:

The first step is to determine the future value of Jill's balance

FV = P (1 + r)^n

FV = Future value  

P = Present value  

R = interest rate  

N = number of years

$866,000(1.09)^8 = $1,725,559.25

the second step is to determine the future value of the balance in Bob's account

$482,000(1.09)^8 = $960,415.19

The difference between Jill and Bob's future value amount is 765,144.06. this has to be the future value of bob's yearly savings

yearly savings = 765,144.06.  / annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

(1.09^8 - 1) / 0.09 = 11.028474

765,144.06.  /  11.028474 = $69,378.96

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