 # Annuity question

The instrument will pay \$20,000 for three years and then \$30,000 in the fourth year. All payments are made at year-end. Required return is 8%. Why do we have 30000 as 30000/(1+.08)^4??? Essentially why does the “4” go with the 30000. Is this b/c we are calculating PV instead of FV? PV=30000/(1+0.08)^4+20000/(1+0.08)^3+20000/(1.08)^2+20000/(1.08)= \$73,592.84 Answer. Thx

Either use your calculator CF function with: CF0=0, CF1=20,000, F1=3, CF2=30,000, F2=1, I=8, CPT NPV (that’s for a BAII Plus) or draw a time line: 0______________1______________2__________________3_______________4 ____________20,000__________20,000_____________20,000____________30,000 20/(1.08)^1+ 20/(1.08)^2 + 20/(1+0.08)^3+ 30/(1+0.08)^4= NPV=73,529.84 Take care clear your previous entries in your CF! Unlike others who are not! (me that is) Remember you get each amount at the end of your period (unlike an annuity due).

map1 drew it perfectly when you are talking about the PV. If you want to calculate the FV of the cash stream at t=4, the answer will be \$30,000+ \$20,000(1.08)+\$20,000(1.08)^2+\$20,000(1.08)^3 It really depends on what the question asked for, the PV or the FV. It does look like they were asking for the PV though since I suspect that you are supposed to calculate the fair value of the instrument?