Question

A 10-year annuity of twenty $10,000 semiannual payments will begin 11 years from now, with the first payment coming 11.5 years from now.

a. If the discount rate is 9 percent compounded monthly, what is the value of this annuity 8 years from now?

b. What is the current value of the annuity?

Answer 1

Given about a 10 year annuity,

payments are semiannual,

PMT = $10000

1st payment will be at 11.5 years from now

discount rate = 9% compounded monthly

So, effective annual rate EAR = (1+APR/n)^n - 1 = (1+0.09/12)^12 - 1 = 9.38%

So, semiannual rate r = ((1+EAR)^(1/2)) - 1 = ((1.0938^(1/2))) - 1 = 4.59%

So, value of annuity at year 11 using ordinary annuity formula is

PV11 = PMT*(1 - (1+r)^(-N))/r = 10000*(1 - (1.0459)^(-20))/0.0459 = $129124.06

1). so value of this annuity at year 8 = PV11/(1+r)^6 = 129124.06/1.0459^6 = $98670.02

2). current value of annuity = PV11/(1+r)^22 = 129124.06/1.0459^22 = $48157.06