Sarah Wiggum would like to make a single investment and have $2.4 million at the time of her retirement in 40 years. She has found a mutual fund that will earn 5 percent annually. How much will Sarah have to invest today? If Sarah invests that amount and could earn a 15 percent annual return, how soon could she retire, assuming she is still going to retire when she has $2.4 million?

The correct answer for present value is 340,909.64 and for time is 13.96 years.

Explanation:

According to the scenario, the given data are as follows:

Future value (A) = $2,400,000

Rate of interest (r) = 5% or 0.05

Time period = 40 years

So, we can calculate present value by using following formula:

P = A / ((1 + r) ^t)

= 2,400,000 / ((1 + 0.05) ^40)

= 2,400,000 / 7.03998871212

= 340,909.64

Now, we calculate time at 15% rate then,

A = P (1 + r) ^t

where, P = 340,909.64

r = 15% or. 15

A = $2,400,000

So, by putting the value we get,

$2,400,000 = 340,909.64 (1 + 0.15) ^t

t = log (2400000/340,909.64) / log (1.15)

t = 13.96 years