An annuity due is annuity whose payment is due immediately at the beginning of each period.
r = 6% = 0.06
compound quarterly
m = 4
PMT = 1200
t = 10 years
n = t × m = 10 × 4 = 40
Present value PV
PV = 1200 + 1200 × [tex]\sf\large{ \left[ \frac{1-(1+0.06)^{-(40-1)}}{0.06} \right]}[/tex]
[tex]\sf{=\:1200+ 1200 × \left[ \frac{1-(1.06)^{-39}}{0.06} \right] = 1200 + 1200 × \left[ \frac{1 - 0.103}{0.06} \right]}[/tex]
= 1200 + 1200 × 14.949 = 19138.89
Answer: 19,138.89
