Final answer:
To calculate the future value of regular quarterly payments into an IRA, one needs to use the future value of an annuity formula with the given interest rate and compounding frequency. The example calculation uses a 55% annual interest rate, compounded quarterly, which is unusually high for financial planning.
Step-by-step explanation:
To calculate the future value of a series of quarterly payments into an Individual Retirement Account (IRA) with compound interest, we use the future value of an annuity formula. In this case, with a deposit of $12,000 per year, the person makes quarterly payments of $3,000 at an interest rate of 55% per annum, compounded quarterly, until they reach age 65.
Let's break it down into a formula:
- P = quarterly payment = $3,000
- r = quarterly interest rate = 55% / 4
- n = total number of quarters
- t = years till retirement = 65 - 40 = 25 years
Using the future value for an ordinary annuity formula:
FV = P * [((1 + r)ⁿ - 1) / r]
First, we need to find n, which is the number of quarters (4 quarters/year * 25 years = 100 quarters) and r, the quarterly interest rate (55% / 4 = 13.75% or 0.1375 as a decimal).
The calculation becomes:
FV = $3,000* [((1 + 0.1375¹⁰⁰ - 1) / 0.1375]
After calculating the future value (FV), we subtract the total contributions (quarterly payment times number of quarters) from the FV to find the total amount of interest earned.
However, keep in mind that a 55% annual interest rate is exceptionally high and not realistic in most financial contexts.