Question

john wishes to pay $1000 a year for 3 years, starting 5 years from today. interest rates are forecast at 2% compounded monthly over the next two years and 4% compounded monthly there after. how much must he set aside today?

Answer 1

Assume that the amount of money John must set aside today is X

To know the amount of money John must set aside today; we have to calculate the present value of all future cash flows

The cash flows are expected as follows –

Year	Cash Flows
0	-X
1
2
3
4
5	$1000
6	$1000
7	$1000

As the interest rates are compounded monthly therefore

Effective annual interest rate = (1+ Annual interest rate/12) ^12 – 1

If annual interest rates are 2%

Effective annual interest rate = (1+ 2%/12) ^12 – 1

= 2.02%

If annual interest rates are 4%

Effective annual interest rate = (1+ 4%/12) ^12 – 1

= 4.07%

Now first we have to discount the cash flows at the rate of 4.07%; to calculate the value at the end of year 2. In following manner

$1000/ (1+4.07%) ^ (5-2) + $1000/ (1+4.07%) ^ (6-2) + $1000/ (1+4.07%) ^ (7-2)

= $887.10 + $852.37 + $819.00

= $2,558.47

After that it will be discounted to present value (year 0) to get the value of X at the rate of 2.02% in following manner

X = $2,558.47/ (1+ 2.02%) ^ 2

X =$2,458.23

Therefore the amount of money John must set aside today is $2,458.23