Question

An investment will pay $150 at the end of each of the next 3 years, $300 at the end of Year 4, $350 at the end of Year 5, and $450 at the end of Year 6. If other investments of equal risk earn 6% annually, what is this investment's present value? Its future value?

Answer 1

Present value of the investment can be calculated with below formula-

Where,

PV = present value

FV = Future value

r = rate of return

n = no. of years

With help of above formula, present value of each year is calculated.

For ex-

Present value of year 2 = 150 / (1+0.06)² = 133.499466 $

Like that present value for all the years is calculated.

year	cashflow ($)	present value of cashflow ($)
1	150	141.509434
2	150	133.499466
3	150	125.9428925
4	300	237.628099
5	350	261.5403605
6	450	317.2322432
	Total	1217.352495

Hence the Present value of the investment = $ 1217.35 (approx)

For calculating future value, below formula can be used-

FV = PV (1 + r )ⁿ

For calculation future value of first year cash flow at end of 6th year, it will be compounded for 5 years (as the cash flow is received at end of 1st year) i.e 150* (1 + 0.06)⁵ = 200.733 $ (approx)

For calculation future value of second year cash flow at end of 6th year, it will be compounded for 4 years (as the cash flow is received at end of 1st year) and like wise for other years.

6th year cash flow will not be compounded as we are calculating future value at end of 6th year.

year	cash flow	Future value of cash flow
1	150	200.7338366
2	150	189.371544
3	150	178.6524
4	300	337.08
5	350	371
6	450	450
	Total	1726.837781

Hence the future value of the investment at end of 6th year = $ 1726.84 (approx)

Hope it helps!