A 5-year annuity of ten $7,800 semiannual payments will begin 9 years from now,

Question

A 5-year annuity of ten $7,800 semiannual payments will begin 9 years from now, with the first payment coming 9.5 years from now. The discount rate is 13 percent compounded monthly. a. What is the value of this annuity five years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What is the value three years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c. What is the current value of the annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Explanation / Answer

Use PVordinary annuity and half of the 13% discount rate: 0.13/2= 0.065 to reflect the semi-annual nature of the payments, and n = 10< 5 years with 2x per year pmts.
PVoa = PMT [(1 - (1 / (1 + i)^n)) / i]
= 7,800[(1-(1/1.065^10)) / 0.065]
= $56,072.88

2) Keep track of your timeline. Five years from now will be four years away from the nine years away value, so discount it back 4 years (8 periods at the semi-annual rate). 4 years w/ semi-annual compounding...discount rate is 1.045^8
56,072.88/(1.065^8) = $33,880.98

3) Keeping track of the timeline... Three years from now will be 6 years away from the nine years away value, so discount the nine year value back 6 years (12 semi-annual periods).
56,072.88/ 1.065^(6*2)
56,072.88/(1.065^12)
= $26,336.47

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.