An investor wants to receive $10,000 per year for 10 years with the first payment startin five years from today. If the investor can earn a 14% annual return, the amount she will have today is closest to: a) $27,091 b) $30,884 c) $52,161 d) $73,667 I’ll post the answer and what tripped me up in 30 minutes. Peace out, dea
B
B
The annuity is due, so the PV of it is $59,463.72 (put your calculator in begin mode with N=10, PMT=-10,000 and I=14, CPT PV) You PV this amount $59,463.72/(1.14)^5 = $31,023.69, the closest being (b)
The answer is B. First, we need to determine how much the investor needs at the end of year 4 to generate the stream of payments starting at the end of year 5. N=10, FV = 0, i = 14%, PMT = -10,000; calculate: PV = $52,161. That’s the present value at the end of year 4. To get to the PV today, need to discount by (1.14)^4. This gets us to $30,884.
Or think that in a 5 year period, in 1 year February will have 29 days, so 5 years from today is in fact the last day of the fifth year:)
B is the answer. I discounted the PV = $52,161 five years getting answer A. These are layups that I can’t afford to get wrong. Little help please: If the first payment is starting five years from today, why do we discount it back only 4 periods? If t=0 today, and first payment is t=5 then to get back to t=0 wouldn’t you discount it back 5 periods? Thanks, dea
No the first payment is at t=5, so the PV calculated is at t=4. Hence to get current value you discount back 4 periods. If you get confused about the time periods the best thing to do is to draw a time line, it really helps
The $10,000 is an annuity due, not an ordinary annuity since you get the payment in the first day of each of the 10 years. Am I wrong? please correct me!