Final answer:
To value a risk-free investment with future payments, each payment is discounted to present value using the current interest rate. At an 8% rate, the total present value is $257.70, and at a 10% rate, it's $248.68.
Step-by-step explanation:
The student is asking about the valuation of a risk-free investment that pays $100 in each of the next three years. To find the current price of this investment, we discount each payment back to its present value using the risk-free rate set by the Federal Reserve. The present value (PV) of a future payment can be calculated using the formula PV = FV / (1 + r)^n, where FV is the future value of the payment, r is the interest rate, and n is the number of years until the payment is received.
(a) At an 8% interest rate, the current prices of the payments are:
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- PV of first payment: $100 / (1 + 0.08)^1 = $92.59
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- PV of second payment: $100 / (1 + 0.08)^2 = $85.73
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- PV of third payment: $100 / (1 + 0.08)^3 = $79.38
The total current price of the investment is the sum of these three values, which comes to: $92.59 + $85.73 + $79.38 = $257.70.
(b) At a 10% interest rate, the current prices of the payments are recalculated:
The total current price of the investment at the higher interest rate is: $90.91 + $82.64 + $75.13 = $248.68.