Final answer:
After calculating with the designated interest rates, Jim will not have enough money to buy the $1500 car from the first bank, and the second bank, with a lower interest rate, provides even less money, so it is not a better deal either.
Step-by-step explanation:
To determine if Jim will have enough money to buy a car that costs $1500 after 5 years with an initial investment of $1000 at a 5% compounded annually rate, we use the formula for compound interest: A = P(1 + r/n)^(nt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
Using the formula we find:
A = 1000(1 + 0.05/1)^(1*5)
A = 1000(1 + 0.05)^5
A = 1000(1.05)^5
A = 1000 * 1.27628
A = $1276.28
With $1276.28, Jim will not have enough to buy the $1500 car, hence the correct choice is b) No, he won't have enough money with the first bank.
At the interest rate of 4% compounded annually, he would have even less money after 5 years, so the second bank is not a better deal. The correct answer to the second question is d) No, the second bank is not a better deal.