Question

An investment offers $10,000 at the end of each year for ten years. (a) If you can earn 5 percent annually, what is this investment worth today? (b) If you do not spend the annual payment but invest it at 5 percent, how much will you have after the ten years have lapsed?

Answer 1

Given,

Annual payment (A) = $10000

No. of years (n) = 10 years

Solution :-

(a)

Interest rate (r) = 5% or 0.05

Present value = A/r x [1 - (1 + r)^-n]

= $10000/0.05 x [1 - (1 + 0.05)^-10]

= $200000 x [1 - (1.05)^-10]

= $200000 x [1 - 0.61391325354]

= $200000 x 0.38608674646 = $77217.35

This investment is worth $77217.35 today.

(b)

Interest rate (r) = 5% or 0.05

No. of years (n) = 10 years

Future value = A/r x [(1 + r)ⁿ - 1]

= $10000/0.05 x [(1 + 0.05)¹⁰ - 1]

= $200000 x [(1.05)¹⁰ - 1]

= $200000 x [1.62889462675 - 1]

= $200000 x 0.62889462675 = $125778.93

You will have $125778.93 after ten years.