Answer:
The future value of annual $4,500 investments over 40 years, compounded at 7% interest annually, can be calculated using the future value of an annuity formula. This calculation demonstrates the benefit of saving early, utilizing the power of compound interest for retirement planning.
Step-by-step explanation:
The question involves calculating the future value of a series of equal annual investments using the formula for the future value of an annuity due to compound interest. In this scenario, the student plans to invest $4,500 at the end of each year for 40 years at an annual interest rate of 7%. This is a common financial calculation for retirement planning and involves understanding the time value of money.
To calculate the future value (FV) of an annuity when the payments are made at the end of each period, we use the formula:
FV = Pmt x [(1 + r)^n - 1] / r
where:
Pmt = annual payment ($4,500),
r = annual interest rate (7% or 0.07),
n = number of years (40).
By inserting the values into the formula we get:
FV = 4500 x [(1 + 0.07)^40 - 1] / 0.07
This calculation gives us the amount the student will have in their Roth IRA after 40 years.