Question

Compute the future value of an ordinary annuity that pays $100 semiannually for 3 years, given the investment is expected to earn 12% compounded annually.

Answer 1

Annual effective rate = 12%
We need semi-annual effective rate
let us assume semi-annual rate as r
equation would be
12% =(1+ r)^ 2 -1
r =5.830052%
Future Value of an Ordinary Annuity
= C*[(1+i)^n-1]/i
Where,
C= Cash Flow per period
i = interest rate per period =5.830052%
n=number of period =4*3 =12
= $100[ (1+0.05830052)^12 -1] /0.05830052
= $100[ (1.05830052)^12 -1] /0.05830052
= $100[ (1.9738 -1] /0.05830052]
= $1,670.35