Assume that you are 23 years old and that you place $3,000 year-end deposits each year into a stock index fund that earns an average of 9.5% per year for the next 17 years. how much money will be in the account at the end of 17 years.
$3,000 • 38.71349998 = $116,140.50
To calculate the amount of money in the account at the end of 17 years, we can use the formula for calculating the future value of an investment with regular contributions.
The formula is:
FV = P * (1 + r)^n - 1 / r
Where:
FV = future value
P = annual deposit
r = interest rate (as a decimal)
n = number of years
Given:
Age = 23 years
Annual deposit = $3,000
Interest rate = 9.5% = 0.095 (as a decimal)
Number of years = 17
First, let's calculate the future value of the annual deposit using the formula:
FV_deposits = P * (1 + r)^n - 1 / r
FV_deposits = $3,000 * (1 + 0.095)^17 - 1 / 0.095
Now, let's calculate the future value of the interest earned on the deposits:
FV_interest = (FV_deposits * (1 + r)^n - 1) / r
FV_interest = (FV_deposits * (1 + 0.095)^17 - 1) / 0.095
Finally, the total future value of the account is:
FV = FV_deposits + FV_interest
Now plug in the calculated values:
FV = $3,000 * (1 + 0.095)^17 - 1 / 0.095 + ((FV_deposits * (1 + 0.095)^17 - 1) / 0.095)
By evaluating this expression, we can find the amount of money that will be in the account at the end of 17 years.