Question

You have just received a windfall from an investment you made in a​ friend's business. He will be paying you $ 10 comma 000 at the end of this​ year, $ 20 comma 000 at the end of the following​ year, and $ 30 comma 000 at the end of the year after that​ (three years from​ today). The interest rate is 3.5 % per year. a. What is the present value of your​ windfall? b. What is the future value of your windfall in three years​ (on the date of the last​ payment)?

Answer 1

a.The present value is $55.39 comma 000

b.The future value is $61.05 comma 000

Step-by-step explanation:

a. the present value for this windfall of the investment will be calculated using the present value formula which is
`Pv = Fv/(1+i)^n`

Pv depicts the present value which we are looking for,

Fv is the future value of the payments the individual receives which are $10 comma 0000 , $20 comma 000 and $30 comma 000.

i represents the interest rate per period which is 3.5%.

then we substitute these values on the above mentioned formula (values in comma 000):

Pv= $10/(1+3.5%) + $20/(1+3.5%)^2 + $30/(1+3.5%)^3

=$55.39 comma 000

that is the present value so we actually added the different present values for the amounts of the future values cause we get them in different times and they not the same.

b. we will use the future value formula to get the future value of the windfall which is
`Fv = Pv(1+i)^n`

which the values still represent the above mentioned values so we substitute ( values in comma 000):

Fv= $10(1+3.5%)^1 + $20(1+3.5%)^2+ $30

= $61.05 comma 000

we add future values for the three different amounts but we are told that we need to calculate the windfall value at the date of the last payment so $30 comma 000 will not accumulate any interest because we they will do that payment on the day they say we must calculate the value of the windfall on.