Final answer:
To calculate the total amount Ralph will have accumulated six years after the last deposit, we can use the formula for compound interest. Ralph has been making deposits of $360 at the end of every quarter for a total of 9 years, with an interest rate of 5% compounded annually. The total amount accumulated after 6 years will be approximately $16,829.34.
Step-by-step explanation:
To calculate the amount Ralph will have accumulated six years after the last deposit, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the total amount of money accumulated after time t
P is the principal amount (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, Ralph has been making deposits of $360 at the end of every quarter for a total of 9 years. The interest rate is 5% compounded annually.
First, let's calculate the number of quarters over the 9-year period:
Number of quarters = 9 years * 4 quarters per year = 36 quarters
Next, let's calculate the principal amount:
Principal amount = $360 * 36 = $12,960
Finally, we can calculate the total amount accumulated after 6 years:
Total amount = $12,960 * (1 + 0.05)^6 = $16,829.34
Therefore, Ralph will have accumulated approximately $16,829.34 six years after the last deposit.