Final answer:
After 20 years, with a 7.0 percent interest rate, an annual contribution of $4,600 to a ROTH IRA will yield approximately $115,597.46, calculated using the future value formula for an annuity.
Step-by-step explanation:
The question seeks to determine the future value of an annual $4,600 contribution to a ROTH IRA over 20 years with a 7.0 percent interest rate. This is a compound interest problem, and the solution can be found using the future value formula for an annuity:
FV = P × {[(1 + r)n - 1] / r},
where FV is the future value, P is the annual payment, r is the annual interest rate (expressed as a decimal), and n is the number of payments (years).
Plugging in the values, we get:
FV = $4,600 × {[(1 + 0.07)20 - 1] / 0.07}
FV = $4,600 × {[(1.07)20 - 1] / 0.07}
FV = $4,600 × {2.75911 - 1} / 0.07
FV = $4,600 × 25.1301
FV = $115,597.46
Therefore, after 20 years, you will have approximately $115,597.46 in your ROTH IRA account, rounded to the nearest penny.