Question

nd the present value of $2,500 under each of the following rates and periods: (Use 365 days for calculation. If you solve this problem with algebra round intermediate calculations to 4 decimal places, in all cases round your final answer to the nearest penny.) a. 8.9 percent compounded monthly for five years. Present value $ b. 6.6 percent compounded quarterly for eight years. Present value $ c. 4.3 percent compounded daily for four years. Present value $ d. 5.7 percent compounded continuously for three years. Present value $ Click if you would like to Show Work for this question: Open Show Work Link to Text Question Attempts: 0 of 2 used Save for later Submit Answer

Answer 1

FV = $2500

PV = FV/(1 + r)ⁿ

a. 8.9 percent compounded monthly for five years.

PV = FV/(1 + r)ⁿ

FV = $2,500, n = 5 * 12 months = 60 months, r = 8.9%/12 (monthly) = 0.7417%

PV = 2500/(1 + 0.7417%)⁶⁰ = $1,604.69 --> Answer

b. 6.6 percent compounded quarterly for eight years.

PV = FV/(1 + r)ⁿ

FV = $2,500, n = 8 * 4 quarters = 32 quarters, r = 6.6%/4 (quarterly) = 0.0165%

PV = 2500/(1 + 0.0165%)³² = $1,480.82 --> Answer

c. 4.3 percent compounded daily for four years.

PV = FV/(1 + r)ⁿ

FV = $2,500, n = 4 * 365 days = 1460 days, r = 4.3%/365 (daily) = 0.0118%

PV = 2500/(1 + 0.0118%)¹⁴⁶⁰ = $2,104.97 --> Answer

d. 5.7 percent compounded continuously for three years.

PV = FV/e^rt

PV = 2500/e^{(5.7% * 3)}

PV = 2500/1.1865

PV = $2,107.05--> Answer