Question

How much will Fortnite Corp. have to invest every 4 weeks, beginning 2 years from now, to accumulate $2,700,000 in 15 years if it deposits $25,000 today into a fund that pays a return of 9.45% compounded continuously? Assume 52 weeks in a year.

a.) $7,904 b.) $7,841 c.) $8,465 d.) $8,402 e.) $8,340 f.) $7,966

Answer 1

Solution:

Future Value of annuity = $2,700,000

We are investing for a period of 13 years as we start from year 2 till year 15.

We have invested $25000 today and will start depositing after 2 years till 15.

Interest rate = 9.45% per annum

Interest rate per 4 week = 9.45% * 4/52 = 0.7269%

Future Value of $25000 , Period = 15 year =15*52 / 4 = 195 period

= 25000 * (1+ 0.7269%)^195 = 102642

Now we will need $2700000 -102642 = 2,597,358 from the investment per 4 week and we have 13*52/4 = 169 period

Using future value of annuity formula

FV = payment *{(1+r)^period - 1}// r

2,597,358 = P *[(1+0.7269%)^169 - 1] / 0.7269%

2,597,358 = P * (3.4 -1) / 0.7269%

P = 2,597,358 / 330.3 = 7861

Option B is closest to 7861, Answer should be 7861