Final answer:
To find out how long it will take for the account to be worth at least $150,000, use the formula for compound interest and solve for the number of quarters. To find the total value of the account after 15 more years, use the formula for compound interest with an increased contribution amount.
Step-by-step explanation:
(a) To find out how many quarters it will take until the account is worth at least $150,000, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the final amount
- P is the initial principal
- r is the annual interest rate (as a decimal)
- n is the number of times that interest is compounded per year
- t is the number of years
Given that the business owner contributes $4,000 at the end of each quarter and the interest rate is 6% compounded quarterly, we have:
A = 4000(1 + 0.06/4)^(4t)
We can solve for t by setting the equation equal to $150,000 and solving for t.
(b) To find the total value of the account after 15 more years, we can use the same formula for compound interest with an increased contribution amount of $8,000:
A = 8000(1 + 0.06/4)^(4(15))