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? (The number of years form age 20 to 65))
what is
10( 1.015^540 - 1)/.015 ?
(don't be surprised if you get over 2 Million dollars)
To calculate the future value of Tim's 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 account
P = the initial deposit (or principal)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
In this case, Tim deposits $10 every month, so the principal (P) is $10. The annual interest rate (r) is 18% or 0.18 in decimal form. Since interest is compounded monthly, the number of times compounded per year (n) is 12. And finally, the number of years (t) is 45.
Substituting these values into the formula, we get:
A = 10(1 + 0.18/12)^(12*45)
First, let's simplify the monthly interest rate (0.18/12):
0.18/12 = 0.015
Now we can calculate the exponent:
12*45 = 540
Substituting the simplified values:
A = 10(1 + 0.015)^(540)
Next, let's calculate the expression inside the parentheses:
1 + 0.015 = 1.015
Now we can raise this value to the power of 540:
1.015^(540) ≈ 209.5990746
Lastly, multiply this value by the principal ($10):
A = 10 * 209.5990746 ≈ $2095.99
Therefore, the amount in Tim's retirement account after 45 years will be approximately $2095.99.