Question

Find the future value of an annuity due of $400 each quarter for 4 1 2 years at 13%, compounded quarterly. (Round your answer to the nearest cent.)

Answer 1

Answer:

$9891.23

Step-by-step explanation:

The formula for future value of annuity due is:

$FV=P[\frac{(1+r)^{n}-1}{r}]*(1+r)$

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 $\frac{13}{4}=3.25$ percent per period(quarter))
• n is the number of periods (here the annuity is for $4\frac{1}{2}$ years, which is $4\frac{1}{2}*4=18$ periods, since quarterly and there are 4 quarters in 1 year)

Substituting all those values in the equation we get:

$FV=400[\frac{(1+0.0325)^{18}-1}{0.0325}]*(1+0.0325)\\=400[23.9497]*(1.0325)\\=9891.23$

Hence, the future value of the annuity due is $9891.23