Question

Suppose that a risk-free investment will make three future payments of $250 in one year, $250 in two years, and $250 in three years

Answer 1

The present price of the risk-free investment is approximately $621.71, assuming an 8% annual interest rate.

Since the given series of payments of $250 each year represents an equal amount paid periodically, it can be referred to as an annuity. The price of the investment (or annuity) today is given as:

P = 1 − (1 + i)−n i × R

Where:

P = Present price or value

i = Interest rate

n = Number of years

R = Annual payment

Plugging in the given values:

P = 1 − (1 + 8%)−3 8% × $250

P ≈ $621.71

Therefore, the present price of the risk-free investment, assuming an annual interest rate of 8%, is approximately $621.71.

Answer 2

Missing part of the question: If the risk-free interest rate is 8%, what is the current value of the investment?

Solution:
PV = FV/(1+r)^n, PV = Present value, FV = Future value, r = interest rate, n = number of years

Therefore,
PV = 250/(1+0.08)^1 + 250/(1+0.08)^2 + 250/(1+0.08)^3 = $644.27