An investor can invest $1000 at the start of a certain year,then $1000 the end of that year and the next year in a certain business.The business guarantees that the investor will receive a payment at the end of the year in five years.What is the future value (FV)of that payment if the investor is to break even,given that the discount rate over those five years is 6% per year?
A)$2002
B)$2681
C)$3000
D)$3792
E)$3370

Question

Quizplus · Accepted Answer

In order for the investor to break even, the present value of the three investments ($1000 at the start, $1000 at the end of year 1, and $1000 at the end of year 2) must equal the present value of the future payment received in year 5. 
Using the formula for present value of a future payment: PV = FV/(1+r)^n 
where PV is the present value, FV is the future value, r is the interest rate or discount rate, and n is the number of years,
we can find the present value of the three investments as follows:

PV1 = $1000 
PV2 = $1000/(1+0.06) = $943.40 
PV3 = $1000/(1+0.06)^2 = $890.00

The total present value of the investments is: 
PV_total = PV1 + PV2 + PV3 = $2833.40

This must equal the present value of the future payment received in year 5, so we can solve for the future value (FV) as follows:
PV_total = FV/(1+0.06)^5 
FV = PV_total x (1+0.06)^5 = $3791.54

Rounding this to the nearest dollar gives the answer of $3792, which is choice D.

An Investor Can Invest $1000 at the Start of a Certain