A 10-year annuity pays $2,100 per month at the end of each month. If the discount rate is 8 percent compounded monthly for the first seven years and 8 percent compounded monthly thereafter, what is the present value of the annuity?
PV for first 7 years
r=7%
Monthly discount rate=7%/12=0.5833%
n=7*12=84
PVat the end of year 7= A*(1-(1+r)^-n)/r
=2100*(1-(1+0.5833%)^-84)/0.5833%
=2100*(1-1.005833^-84)/0.005833
=2100*(1-0.6135)/0.005833
=2100*0.3865/0.005833
=$139142.1
PV for last 3 years
monthly rate=8%/12=0.67%
n=3*12=36
PV= A*(1-(1+r)^-n)/r
=2100*(1-(1+0.67%)^-36)/0.67%
=2100*(1-1.0067^-36)/0.0067
=2100*(1-0.7863)/0.0067
=2100*0.2137/0.0067
=$66975.35
PV at the end of year 0=66975.35*(1+0.5833%)^-84=66975.35*0.6135=$41090.46
Total PV=139142.1+41090.46= $180232.56
Get Answers For Free
Most questions answered within 1 hours.