Question

A 20-year annuity of forty $11,000 semiannual payments will begin 9 years from now, with the first payment coming 9.5 years from now. Required : (a) If the discount rate is 12 percent compounded monthly, what is the value of this annuity 4 years from now? (b) What is the current value of the annuity? rev: 09_17_2012

Answer 1

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

Effective Annual Rate = ((1+12/12*100)^12-1)*100

Effective Annual Rate% = 12.68

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

PV= 11000*((1-(1+ 12.68/200)^(-20*2))/(12.68/200))

PV = 158661.46

THis is the value at beginning of year 9

For PV at end of year 4

Future value = present value*(1+ rate)^time

158661.46 = Present value*(1+0.1268)^5

Present value = 87344.84

PV today

Future value = present value*(1+ rate)^time

158661.46 = Present value*(1+0.1268)^9

Present value = 54181.36