At age 25 someone sets up an IRA (individual retirement account) with an APR of 4%. At the end of each month he deposits $85 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.
I am trying to figure out after retirement how much $ the IRA will contain
How would I find the total deposit made over the time period?
i = .04/12 = .00333...
n = age(65 - 25) * 12 = 480 payments
You need to use the "amount of an annuity" formula
amount = 85(1.003333...^480 - 1)/.003333...
= 100,466.72
not going to get you very far into retirement. Better increase your payment.
To calculate the amount the IRA will contain at retirement, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/IRA
P = the initial deposit
r = annual interest rate (expressed as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, the initial deposit is $0, as the person sets up the IRA at age 25. The monthly deposit is $85, and the annual interest rate is 4%. We need to calculate the number of times interest is compounded per year and the number of years until retirement.
Since the monthly deposit is made at the end of each month, the interest is compounded monthly. Therefore, the interest is compounded 12 times per year (n = 12).
The number of years until retirement is calculated by subtracting the current age (25) from the retirement age (65).
Let's calculate the future value of the IRA:
n = 12 (monthly compounding)
r = 4% = 0.04
t = 65 - 25 = 40 years
A = $85(1 + 0.04/12)^(12 * 40)
Using a calculator, the future value of the IRA is approximately $145,251.67.
To compare this amount to the total deposits made over the time period, we can calculate the total deposits made throughout the 40-year period. Since $85 is deposited at the end of each month, there are 12 months in a year, so the number of deposits made will be 12 * 40 = 480 deposits.
Total deposits made = $85 * 480 = $40,800.
Therefore, at retirement, the IRA will contain approximately $145,251.67, while the total deposits made over the 40-year period will be $40,800.
To calculate the amount the IRA will contain when the individual retires at age 65, we need to consider the monthly contributions made to the account and the interest earned over a 40-year period.
First, let's calculate the number of months between the age of 25 and 65:
40 years × 12 months/year = 480 months
Next, calculate the future value of the IRA, taking into account the monthly deposits and the 4% annual percentage rate (APR). To do this, we can use the future value of an ordinary annuity formula:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future Value of the IRA
P = Monthly deposit ($85)
r = Monthly interest rate (APR/12)
n = Number of months (480)
Let's plug in the values into the formula:
r = 4% / 12 = 0.04 / 12 = 0.00333 (approx.)
n = 480
FV = 85 * ((1 + 0.00333)^480 - 1) / 0.00333
Calculating this equation will give you the amount the IRA will contain at retirement.
To compare this amount to the total deposits made over the time period, you can multiply the monthly deposit amount by the number of months:
Total Deposits = Monthly Deposit * Number of Months
Total Deposits = $85 * 480
This will give you the total amount deposited into the IRA over the 40-year period.
Comparing the amount contained in the IRA at retirement to the total deposits will give you an idea of how much interest has been earned.
Please note that this calculation assumes that the interest is compounded monthly and that no withdrawals are made from the IRA during the accumulation period.