Question

Andrew Bogut just received a signing bonus of 1,000,000. His plan is to invest this payment in a fund that will earn 8%, compounded annually.

a) If Bogut plans to establish the AB Foundation once the fund grows to 1,999,000, how many years until he can establish the foundation?

b) Instead of investing the entire 1,000,000, Bogut invests 300,000 today and plans to make 9 equal investments into the fund beginning one year from today. What amount should the payments be if Bogut plans to establish the 1,999,000 foundation at the end of 9 years.

Answer 1

Here,

Present value = 1 million

Annual return = 8%

a.

Future Value = 1.999 million

Now,

FV = PV x (1+r)^n

Hence, FV / PV = (1+r)^n

Hence, 1.999 / 1 = (1.08)^n

1.999 = (1.08)^n

Solving this we get n = 8.9997 years = ~9years

Also, here we can use the thumb rule of 72, where dividing 72 by 8% we get 9 years (this rule gives approximate value)

This can also be solved using excel

time = nper (8%, 0, -1, 1.999,0)

b.

Future value of 300,000 after ten years = 300000 x (1+0.08)^10

FV = 647,677

Hence, remaining amount = 1,999,000 - 647,677 = 1,351,323

Using excel to find the payment value

payment = pmt (rate, years, pv, -fv, 1)

payment = pmt (8%, 9, 0, 1351323,1)

Payment = 100198