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Jim places $1000 in a bank account that pays 5% compounded annually. After 5 years, will he have enough money to buy a car that costs $1500? If another bank will pay Jim 4% compounded annually, is this a better deal?

a) Yes, he will have enough money with the first bank
b) No, he won't have enough money with the first bank
c) Yes, the second bank is a better deal
d) No, the second bank is not a better deal

1 Answer

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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.

User Anna Pawlicka
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