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The present value of $100 expected two years from today at a discount rate of 6 percent is

A) $106.00.
B) $89.00.
C) $112.36.
D) $100.00

1 Answer

3 votes

Final answer:

The present value of $100 expected two years from today at a 6 percent discount rate is $89.00, which is obtained using the present value formula and rounding the result to two decimal places.

Step-by-step explanation:

The present value of $100 expected two years from today at a discount rate of 6 percent is calculated using the present value formula: PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the discount rate, and n is the number of periods. Applying this formula:

PV = $100 / (1 + 0.06)^2
PV = $100 / (1.1236)
PV = $88.99 (rounded to two decimal places)

Therefore, the correct answer is B) $89.00.

For additional clarity, here's an example with a two-year bond issued for $3,000 at an interest rate of 8%. After the first and second years, the bond pays $240 in interest. At the end of the second year, the bond also returns the $3,000 principal. The present value, if discounted at the same 8%, would be calculated by adding the present value of the interest payments and the principal amount. However, if the discount rate changes to 11%, these amounts would be worth less in present value terms.

User Johannes Staehlin
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