At age 18, someone sets up an IRA (individual retirement account) with an APR of 4%. At the end of each month he deposits $40 in the account. How much will the IRA contain when he retires at age 65? Compare that amount to the total deposits made over the time period.
just plug your numbers into the future value formula for annuities.
deposits made are (65-18)*12*40
To calculate the future value of the IRA account, we can use the formula for compound interest:
FV = P * (1 + r/n)^(n*t)
Where:
FV = future value
P = principal amount (initial deposit)
r = annual interest rate (expressed as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, the principal amount is $40, the annual interest rate is 4% (or 0.04 as a decimal), and the interest is compounded annually. The time period is 65 - 18 = 47 years.
FV = $40 * (1 + 0.04/12)^(12*47)
FV = $40 * (1.003333)^564
FV = $40 * 360.40407074
FV ≈ $14,416.16
So the IRA will contain approximately $14,416.16 when he retires at age 65.
To determine the total deposits made over the time period, we can multiply the monthly deposit amount by the number of months:
Total deposits = $40 * 12 * 47
Total deposits = $22,560
Therefore, the IRA will contain more money ($14,416.16) than the total deposits made ($22,560) over the time period.