Tim deposits $10 every month into a retirement account which averages 18% interest compounded monthly. How much will be in this account after 45 years?
To find out 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/amount in the account after time t
P = the principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = time in years
In this case:
P = $10 (monthly deposit)
r = 18% = 0.18 (annual interest rate)
n = 12 (compounded monthly)
t = 45 (years)
Using these values, we can plug them into the formula:
A = 10(1 + 0.18/12)^(12*45)
Calculating the expression inside the parentheses first:
1 + 0.18/12 = 1.015
Now, we can substitute the values into the formula and calculate the future value of the retirement account:
A = 10 * (1.015)^(540)
A ≈ $187,811.74
Therefore, after 45 years of monthly deposits of $10 into an account with an average interest rate of 18% compounded monthly, the amount in the retirement account will be approximately $187,811.74.