Question

In this paper you will be working with a dollar value of $1,000,000 to calculate present value, present value of an annuity, future value and future value of an annuity. In each of the four parts of the assignment, you will provide a scenario in which you personally or a business would need to calculate these values. Personal examples are planning for retirement, planning for education or winning the lottery. Business examples are buying a new delivery truck, bond issues, purchasing a new building or opening a start-up business. The example you use is your choice and you may use the same example or different examples for each of the four calculations. For each of the four calculations, you will need to determine the timeline (how many years) and the interest rate. Research current interest rates to determine a reasonable percentage.

Answer 1

Present value of a single sum

Let us find the Present value of $ 1000000 that is to be received at end of year 8 as proceeds from a bond investment & the interest rate we use is the interest on one other investment owned, ie. 9%p.a.

we need to use the formula, to find the present value of a single sum in future

ie. PV= FV/(1+r)^ n

where, PV= the present value --to be found out-----??

FV= the future value, ie $ 1000000

r= the interest rate p.a., ie.9%

n= no.of years = 8

so, plugging -in all the values, in the formula,

PV=1000000/(1+0.09)^ 8

501866.28

So, the Present value of $ 1000000 that is to be received at end of year 8 at 9% p.a.= $ 501866

Present value of annuity---- a series of amounts

Now,instead of receiving at end yr. 8, we are going to receive $ 180675 at the end of each year for 8 years

& using the same 9% interest as above,

we will find the present value of this annuity

using the formula,

PV of annuity=Pmt.(1-(1+r)^-n)/r

where PV=the present value to be found out--??

Pmt.= the annuity received at end of each yr. for 8 yrs.= $ 180675

r=rate of interest used= 9%

n=no.of compounding years, 8

so, plugging -in all the values, in the formula,

PV of annuity=180675*(1-(1+0.09)^-8)/0.09=

1000003

So, the present value of this annuity = $ 1000000

Future value of a single sum

Now, we are investing $1000000 in a security that will mature at end of year 8 , interest at 9% p.a. to be received along with the principal

we need to use the formula, to find the future value of this single sum, to know how much we will receive in total

ie. FV=PV*(1+r)^n

where, PV= the present value of the investment, ie. $ 1000000

FV= the compounded future value--- to be found out---??

r= the interest rate p.a., ie.9%

n= no.of years = 8

so, plugging -in all the values, in the formula,

ie. FV=1000000*(1+0.09)^8=

1992562.64

So, the Future value of $ 1000000 , or the amount accumulated , that is to be received at end of year 8 at 9% p.a.= $ 1992563

Future value of annuity------- a series of amounts

Now, we are going to recive $ 90675 at every year-end for 8 years

& using the same 9% interest as above,

we will find the future value of these series of receipts

using the formula,

FV of annuity=Pmt.((1+r)^n-1)/r

where FV=the future value to be found out--??

Pmt.= the annuity received at end of each yr. for 8 yrs.= $ 90675

r=rate of interest used= 9%

n=no.of compounding years, 8

so, plugging -in all the values, in the formula,

FV of annuity=90675/(1+0.09)^8-1)/0.09

1000007

So, the Future value of this series of receipts (annuity )= $ 1000007