Question

​(Future value​) Sarah Wiggum would like to make a single​ lump-sum investment and have ​$1.7 million at the time of her retirement in 28 years. She has found a mutual fund that expects to earn 5 percent annually. How much must Sarah invest​ today? If Sarah earned an annual return of 16 ​percent, how much must she invest​ today?

1. If Sarah can earn 5 percent annually for the next 28 ​years, how much will she have to invest​ today?

$ ​(Round to the nearest​ cent.)

2. If Sarah can earn 16 percent annually for the next 28 ​years, how much will she have to invest​ today?

$ (Round to the nearest cent.)

Answer 1

Part A:

Present Value:

Present value is current value of Future cash flows discounted at specified discount Rate.

PV = FV / (1+r)^n
Where r is Int rate per period
n - No. of periods

Particulars	Amount
Future Value	$      1,700,000.00
Int Rate	5.0000%
Periods	28

Present Value = Future Value / ( 1 + r )^n
= $ 1700000 / ( 1 + 0.05 ) ^ 28
= $ 1700000 / ( 1.05 ) ^ 28
= $ 1700000 / 3.9201
= $ 433659.18

Part B:

Present Value:

Particulars	Amount
Future Value	$      1,700,000.00
Int Rate	16.0000%
Periods	28

Present Value = Future Value / ( 1 + r )^n
= $ 1700000 / ( 1 + 0.16 ) ^ 28
= $ 1700000 / ( 1.16 ) ^ 28
= $ 1700000 / 63.8004
= $ 26645.58