Answer:
$9891.23
Step-by-step explanation:
The formula for future value of annuity due is:
[tex]FV=P[\frac{(1+r)^{n}-1}{r}]*(1+r)[/tex]
Where,
- FV is the future value of the annuity (what we need to find)
- P is the periodic payment (here it is $400)
- r is the interest rate per period (here 13% yearly interest is actually [tex]\frac{13}{4}=3.25[/tex] percent per period(quarter))
- n is the number of periods (here the annuity is for [tex]4\frac{1}{2}[/tex] years, which is [tex]4\frac{1}{2}*4=18[/tex] periods, since quarterly and there are 4 quarters in 1 year)
Substituting all those values in the equation we get:
[tex]FV=400[\frac{(1+0.0325)^{18}-1}{0.0325}]*(1+0.0325)\\=400[23.9497]*(1.0325)\\=9891.23[/tex]
Hence, the future value of the annuity due is $9891.23
