Bob makes his first deposit into an IRA earning % compounded annually on the day he turns 27 and his last deposit on the day he turns 35. (9 equal deposits in all.) With no additional deposits, the money in the IRA continues to earn % interest compounded annually until Bob retires on his 65th birthday. How much is the IRA worth when Bob retires?
You are missing the % for interest and the amount for the annual deposit into the IRA.
plug in 6.4 as the % and $1,000 as the deposit
To calculate the worth of Bob's IRA when he retires, we need to break down the information provided and use the compound interest formula.
1. Bob makes his first deposit on the day he turns 27, and his last deposit on the day he turns 35. This means he makes a total of 9 equal deposits.
2. The interest on the IRA is compounded annually, but the specific interest rate is missing from the question. Let's assume the interest rate is "r".
3. Bob's last deposit is made on the day he turns 35, and he retires on his 65th birthday. Therefore, the money will continue earning interest for 30 years.
Let's calculate the worth of Bob's IRA when he retires:
Step 1: Calculate the contribution made by Bob each year.
Let's assume the annual contribution is "C". Since Bob makes 9 equal deposits over 9 years, the annual contribution can be calculated as:
C = Total Deposits / Number of Years
C = Total Deposits / 9
Step 2: Calculate the value of Bob's IRA after the last deposit.
The amount after the last deposit can be calculated using the compound interest formula:
Value after last deposit = C * [(1 + r)^n - 1] / r
Where n = Number of years (35 - 27) and r = Interest rate as a decimal.
Step 3: Calculate the value of Bob's IRA at retirement.
The amount at retirement can be calculated using the compound interest formula again:
Value at retirement = Value after last deposit * (1 + r)^30
By substituting the above formulas with the given values, you can find the worth of Bob's IRA when he retires. Just make sure to fill in the missing interest rate!
To determine the value of Bob's IRA when he retires, we need to break down the problem into several steps.
Step 1: Calculate the amount accumulated from the initial 9 deposits made from when Bob turned 27 until he turned 35.
To do this, we need the initial deposit amount and the interest rate. However, both the deposit amount and the interest rate are missing from the question. Please provide those values so that we can proceed with the calculation.
Step 2: Determine the total number of years between Bob's 35th and 65th birthdays.
Bob retires on his 65th birthday, so the number of years he keeps the money in the IRA after his 35th birthday is 65 - 35 = 30 years.
Step 3: Calculate the final value of the IRA after compound interest for the 30-year period.
We need two pieces of information to calculate the final value: the interest rate for this period and the amount accumulated from Step 1. Please provide the interest rate, and we can calculate the final value using the compound interest formula:
FV = PV * (1 + r)^n
Where:
FV = Future Value (final value of the IRA)
PV = Present Value (amount accumulated from Step 1)
r = Interest rate (per year, in decimal form)
n = Number of compounding periods (in this case, the number of years)
Please provide the interest rate, and I can provide the final value of Bob's IRA when he retires.