Final answer:
Using the formula for compound interest, the total amount in Luis's college fund at age 18, after accounting for an annual 3.5% interest rate compounded yearly, will be approximately $10,900.96, which does not match any of the options provided.
Step-by-step explanation:
The question involves finding the future value of a sum of money invested at a given interest rate over a certain number of years, using the concept of compound interest. When Luis was 4 years old, his parents put $6,500 into a college fund account that earned 3.5% interest. We want to calculate the total amount in the account when he starts college at 18.
To calculate the future value of the investment, we can use the formula for compound interest, which is A = P(1 + r/n)^(nt), where:
- P is the principal amount ($6,500)
- r is the annual interest rate (3.5% or 0.035)
- n is the number of times interest is compounded per year (assuming it is compounded once a year, so n=1)
- t is the number of years the money is invested (14 years, from age 4 to 18)
By substituting the values into the formula, we have:
A = 6500(1 + 0.035/1)^(1*14)
A = 6500(1.035)^14
A = 6500 * 1.677109
A = $10,900.96 (rounded to two decimal places)
Therefore, the total amount in Luis's account when he starts college will be approximately $10,900.96, which is not an exact match to any of the multiple-choice options provided. It seems there might be a slight discrepancy or rounding issue with the options given.