Tim deposits $10 every month into retirement account which averages 18% interest compounded monthly. How much will be in this account after 45 years? (The number of years from age 20 to 65).
To calculate the amount in the retirement account after 45 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/retirement account
P = the principal amount (the initial deposit or investment)
r = annual interest rate (expressed as a decimal)
n = number of times that interest is compounded per year
t = number of years
In this case, Tim deposits $10 every month, which means the principal (P) is $10 multiplied by the number of months in 45 years. Since there are 12 months in a year, the number of months in 45 years is 45 * 12 = 540 months.
P = $10 * 540 = $5,400
The annual interest rate (r) is 18%, which, in decimal form, is 0.18. The interest is compounded monthly, so the number of times compounded per year (n) is 12.
Now we can plug these values into the formula:
A = $5,400 * (1 + 0.18/12)^(12*45)
Calculating this expression will give us the final amount in the retirement account after 45 years.