David inherited an annuity worth $3,280.16 from his uncle. The annuity will pay

Question

David inherited an annuity worth $3,280.16 from his uncle. The annuity will pay him five equal payments of $800 at the end of each year. The annuity fund is offering a return of David's friend, Sagar, wants to go to business school. While his father will share some of the expenses, Sagar still needs to put in the rest on his own. But Sagar has no money saved for it yet. According to his calculations, it will cost him $38,364 to complete the business program, including tuition, cost of living, and other expenses. He has decided to deposit $5,500 at the end of every year in a mutual fund, from which he expects to earn a fixed 6% rate of return It will take approximately years for Sagar to save enough money to go to business school.

Explanation / Answer

1.) Present value = PMT times (present value annuity factor = n = 5, i = ?)

3,280.16 = 800 (PVA factor n = 5, i = ?)

3,260.16/ 800 = PVA factor n = 5, i = ?

4.075 = PVA factor n = 5, i = ?

Now check from present value annuity table in column states n= 5 and corresponding value is near 4.075.

We get 4.075 value lies near 8%.

Therefore annuity offerring return rate is 8%.

2.) FV = PV (FV factor for n = ? Years, i = 6% per year)

38,364 = 5,500 ( FV factor for n= ? years, i = 6% per year)

38,364/5500 = FV factor for n =? years, i = 6% per year

6.98 = FV factor n= ?years, i = 6% per year

Now we search only 6% column of FV table For the FV factor closest to 6.98. In this case we get n = 6.

Therefore, it will take 6 years to get enough money.

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