Person A opens an IRA at age 25, contributes $2000 per year for 10 years, but makes no additional contributes thereafter. Person B waits untill age 35 to open an IRA and contributes $2000 per year for 30 years. There is no initial investment in either case. Asumming an interest rate of 8%, what is the alance i each IRA at age 65?
To determine the balance in each IRA at age 65, we need to calculate the compound interest accumulated over the specified periods. The formula to calculate the compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan
P = the principal investment/loan amount
r = the annual interest rate (expressed as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
Let's calculate the balances for each IRA step by step:
For Person A:
Principal investment (P) = $2,000
Annual interest rate (r) = 8% = 0.08 (expressed as a decimal)
Number of times interest compounds per year (n) = 1 (since there are no additional contributions)
Number of years (t) = 10
Using the formula:
A = $2,000(1 + 0.08/1)^(1*10)
A = $2,000(1 + 0.08)^10
A = $2,000(1.08)^10
A ≈ $4,661.39
So, at age 65, Person A's IRA balance would be approximately $4,661.39.
Moving on to Person B:
Principal investment (P) = $2,000
Annual interest rate (r) = 8% = 0.08 (expressed as a decimal)
Number of times interest compounds per year (n) = 1 (since there are no additional contributions)
Number of years (t) = 30
Using the formula:
A = $2,000(1 + 0.08/1)^(1*30)
A = $2,000(1 + 0.08)^30
A ≈ $23,802.22
So, at age 65, Person B's IRA balance would be approximately $23,802.22.
Therefore, Person A would have a balance of approximately $4,661.39, and Person B would have a balance of approximately $23,802.22 in their respective IRAs at age 65.