Final answer:
Chris would have approximately $229,572.88 at age 60 after starting with a savings of $300 per month for 10 years and investing the total amount, including the accumulated interest of $4,000, at a 6% annual interest rate compounded over 30 years.
Step-by-step explanation:
When Chris started working at age 20, she began saving $300 per month. This continued for 10 years, accumulating an additional $4,000 in interest by the end of this period. To compute how much money Chris had at age 60, we first need to calculate the total amount saved after the initial 10 years. With $300 saved per month for 120 months (10 years), Chris would have saved $36,000, which when we add the $4,000 interest becomes $40,000.
This $40,000 is then invested at a 6% interest rate compounded annually. The formula for compound interest is A = P(1 + r/n)^(nt), where:
- P is the initial principal balance ($40,000)
- r is the annual interest rate (6% or 0.06)
- n is the number of times that interest is compounded per year (1)
- t is the number of years the money is invested (age 60 - age 30 = 30 years)
Therefore, Chris's investment at age 60 can be calculated as follows:
40,000(1 + 0.06/1)^(1*30) = 40,000(1 + 0.06)^30 = 40,000(1.06)^30
Using a calculator, we find that the total amount Chris would have at age 60 is approximately $229,572.88. Thus, Chris would have $229,572.88 at age 60 due to the power of compound interest working on her initial savings.