Sarah Wiggum would like to make a single investment and have $2 million at the time of her retirement in 35 years. She has found a mutual fund that will earn 4 percent annually. How much will Sarah have to invest today? If Sarah invests that amount and could earn a 14 percent annual return, how soon could she retire, assuming she is still going to retire when she has $2 million?

a) Amount to be invested today = $506,830.9

b) She will retire in 10.5 years time

Explanation:

The amount to be invested by Sara Wiggum today at 4%  to accumulate $2 million in 35 years is called the Present Value.

Present value (PV) is  the discounted value of a future amount at the opportunity cost rate of return .  The amount to be invested now at a particular rate of return to equal a future sum.

Present Value (PV)= (1+r)^(-n) × Future cash flow

For Sarah, the

PV = (1+0.04)× (-35) × 2,000,000

    = 0.2534 × 2,000,000

     = 506,830.9415

Amount to be invested today = $506,830.9

How soon will She retire at rate of 14% per annum?

The PV is still  506,830.9415,

FV is still 2,000,000,

But rate now is - 14%, and

n - ?.  

so we need to work out "n"

Work out "n" as folows:

(1+0.14)^(-n) = 2000000/506,830.9

(1+0.14)^(-n)   = 3.9406

n =  log 3.9406/log 1.14

n = 10.5 years

She will retire in 10.5 years time

Solution please, where did you get .2534?

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