Final answer:
Using the formula for compound interest, Jose would have approximately $750.60 after 6 years of investing $500 at a 7% annual interest rate with annual compounding. The closest answer choice provided is option d. $750.50.
Step-by-step explanation:
The question involves calculating the future value of an investment with compound interest. To find out how much Jose would have after 6 years when he leaves $500 invested at a 7.0% annual interest with annual compounding, we use the compound interest formula:
A = P(1 + r/n)nt
Where:
- A = the future value of the investment/loan, including interest
- P = the principal investment amount (the initial deposit or loan amount)
- r = the annual interest rate (decimal)
- n = the number of times that interest is compounded per year
- t = the number of years the money is invested or borrowed for
In Jose's case:
- P = $500
- r = 7.0% or 0.07
- n = 1 (since it is compounded annually)
- t = 6
So the calculation is:
$500(1 + 0.07/1)1*6 = $500(1 + 0.07)6
Now calculating the compound amount:
A = $500(1.07)6
A = $500 * 1.501209
A ≈ $750.60
Therefore, the correct choice is option d, $750.50 - though there is a slight discrepancy due to rounding during the calculation.