Question

To save money for his daughter's college tuition, Dan invests every quarter in an annuity that pays interest, compounded quarterly. Payments will be made at the end of each quarter. Find the total value of the annuity in years.

Answer 1

The question is incomplete. The complete question is :

To save money for his daughter's college tuition, Dan invests $269 every quarter in an annuity that pays 6.9% interest, compounded quarterly. Payments will be made at the end of each quarter. Find the total value of the annuity in 20 years.

Solution :

Given :

Annuity = $ 269

Compounded quarterly for 20 years, so N = 4 x 20 = 80

Rate of interest = $\frac{6.90 \%}{4}$

                          = 1.725 %

We know Future value of the annuity is given by :

$FV= \text{Annuity} \times \frac{(1+R)^{N-1}}{R}$

$FV= \text{269} \times \frac{(1+1.725\%)^{80-1}}{1.725\%}$

     $=269 \times 169.762413$

     = 45666.09

So the total value of he annuity is $45,666.09