Question 1093018
<br>The formula for the value V of an investment of A made regularly for n years at an interest rate of r is<br>
{{{V = A((1+r)^n-1)/r}}}<br>
Find the value V for your problem where the regular deposit A is 2000, the interest rate is 6% (that is, .06), and the number of years n is 15.<br>
After the regular contributions stop and the money just sits there gaining interest, the compound interest formula for the final value A is the beginning principal P, multiplied by the periodic growth factor (1 plus r, where r is the periodic interest rate; i.e., the annual interest rate divided by the number of periods per year) n times, where n is the number of compounding periods:<br>
{{{A = P(1+r)^n}}}<br>
In your problem, the beginning principle P for these last 10 years is the ending value after the first 15 years, as found previously; the periodic interest rate is  one-quarter of the 8% annual interest rate (again, as a decimal), since compounding is quarterly; and the number of compounding periods n is 40 since the compounding is 4 times a year for 10 years.<br>
As a check for your calculations, I found the value after 15 years to be $46,551.94 and the final value after 25 years to be $102,788.53.