Question

How much money should you save now to have a guaranteed saving of $1,000 per year for 12 years starting next year, at a rate of return of 12% per year?

		$12,600
		$6,200
		$12,000
		$6,000

Answer 1

b. $6200

To get 1000 per year we need to calculate the present value of every 1000 dollar in 12 years

Present value = Future value/(1 + interest rate)^ year

The present value of $1000 received in the first year

=1000/(1+12%)^1

= $892.86

Similarly, we will get the present value of all 12 years

year 2

=1000/(1+12%)^2

= $797.19

Year 3

=1000/(1+12%)^4

= $711.78

Year 4

= 1000/(1+12%)^4

= $635.52

And so on, In the table form:

Year	Cash	PV
1	$1,000.00	$892.86
2	$1,000.00	$797.19
3	$1,000.00	$711.78
4	$1,000.00	$635.52
5	$1,000.00	$567.43
6	$1,000.00	$506.63
7	$1,000.00	$452.35
8	$1,000.00	$403.88
9	$1,000.00	$360.61
10	$1,000.00	$321.97
11	$1,000.00	$287.48
12	$1,000.00	$256.68
Total	$12,000	$6,194.37

Present value PV = 6194.37 so we will save 6200 to get 1000 for 12 years if the interest rate is 12% compounded annually.

You can also use a spreadsheet and use PV formula to get the same result or to check your answer

=pv(12%,12,-1000)