Final answer:
At the age of 35, you would have approximately $6321.74 in your retirement account when you reach the age of 55. By the time you reach age 65, you would have approximately $125,576.03 in your account, considering the monthly deposits and new interest rate.
Step-by-step explanation:
To calculate the amount of money in the retirement account at the age of 55, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the future value of the investment
- P is the principal amount (initial investment)
- r is the annual interest rate (in decimal form)
- n is the number of times that interest is compounded per year
- t is the number of years the money is invested for
In this case:
- P = $2000
- r = 6.5% or 0.065
- n = 12 (compounded monthly)
- t = 55 - 35 = 20 years
Plugging in the values into the formula, we get:
A = $2000(1 + 0.065/12)^(12*20) = $6321.74
Therefore, you would have approximately $6321.74 in the account when you reach the age of 55.
To calculate the amount of money in the account when you reach age 65, we need to use the same formula for compound interest. However, in addition to the initial investment, we also need to consider the monthly deposits and the new interest rate:
- P = $6321.74
- r = 8% or 0.08
- n = 12 (compounded monthly)
- t = 65 - 55 = 10 years
Also, since the deposits are made at the end of each month, the total number of deposits would be 10 * 12 = 120.
Plugging in the values into the formula, we get:
A = $6321.74(1 + 0.08/12)^(12*10) + $400[(1 + 0.08/12)^(12*10) - 1]/(0.08/12)
Simplifying the equation, we get:
A = $125,576.03
Therefore, you would have approximately $125,576.03 in your account when you reach the age of 65.