You are making $1,000 monthly deposits into a fund that pays interest at a rate of
6% compounded monthly. What would be the balance at the end of 10 years?
$163,879.35
To find the balance at the end of 10 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final balance
P is the principal amount (the initial deposit)
r is the annual interest rate (as a decimal)
n is the number of times interest is compounded per year
t is the number of years
In this case, you are making monthly deposits of $1,000, so P = $1,000. The annual interest rate is 6%, or 0.06 as a decimal. Since interest is compounded monthly, n = 12 (the number of months in a year).
Now we can calculate the balance at the end of 10 years:
A = $1,000(1 + 0.06/12)^(12*10)
Let's break it down:
Step 1: Calculate the monthly interest rate
Monthly interest rate = 0.06/12 = 0.005
Step 2: Calculate the compound factor
Compound factor = (1 + 0.005)^(12*10)
Step 3: Calculate the final balance
A = $1,000 * Compound factor
By plugging in the values, we can find the balance at the end of 10 years.