Question

(Related to Checkpoint 5.4) (Present value) Sarah Wiggum would like to make a single investment and have $1.6 million at the time of her retirement in 32 years. She has found a mutual fund that will earn 6 percent annually. How much will Sarah have to invest today? If Sarah earned an annual return of 14 percent, how soon could she then retire? (Round to a. If Sarah can earn 6 percent annually for the next 32 years, the amount of money she will have to invest today is $ the nearest cent.)

Answer 1

This question requires application of basic time value of money function, according to which FV = PV * (1 + r)" where FV is Future Value, PV is present value, n is number of periods and r is rate per period

Question 1:

$1,600,000 = PV * (1 + 6%)³²

$1,600,000 = PV * 6.4534

PV = $247,931.8

Question 2:

$1,600,000 = $247,931.83 * (1 + 14%)ⁿ

6.45 = 1.14ⁿ

Taking log of both sides,

LN(6.45) = n * LN(1.14)

n = 1.8646/0.1310

n = 14.23 years (Please remember the answer need to be entered with appropriate rounding off)