I am SO STUCK on this problem... PLEASE HELP ASAP!!!
Suppose Kevin and Jill both deposit $4000 into their personal accounts. If Kevin’s account earns 5% simple interest annually and Jill’s earns 5% interest compounded annually, how much will each account balance show at the end of 5 years? Calculate the difference between each account.
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To solve this problem, we need to calculate the balance of Kevin's and Jill's accounts after 5 years, using the provided interest rates. Here's how to do it step by step:
1. For Kevin's account, we need to calculate simple interest. Simple interest is calculated using the formula:
Simple Interest = Principal (P) * Rate (R) * Time (T)
Kevin deposits $4000, and the interest rate is 5% or 0.05. The time is 5 years. Plugging these values into the formula:
Simple Interest = $4000 * 0.05 * 5 = $1000
Therefore, Kevin's account balance after 5 years would be $4000 + $1000 = $5000.
2. For Jill's account, we need to calculate compound interest. Compound interest is calculated using the formula:
Compound Interest = Principal (P) * (1 + Rate (R))^Time (T)
Jill also deposits $4000, and the interest rate is still 5% or 0.05. The time is also 5 years. Plugging these values into the formula:
Compound Interest = $4000 * (1 + 0.05)^5
Using a calculator, calculate (1 + 0.05)^5 = 1.27628 (rounded to 5 decimal places).
Compound Interest = $4000 * 1.27628 = $5105.12 (rounded to 2 decimal places).
Therefore, Jill's account balance after 5 years would be $5105.12.
3. To find the difference between each account balance, subtract Kevin's balance from Jill's balance:
Difference = Jill's Balance - Kevin's Balance
Difference = $5105.12 - $5000 = $105.12
Therefore, the difference between Kevin's and Jill's account balances after 5 years is $105.12.
So, at the end of 5 years, Kevin's account balance would show $5000 and Jill's account balance would show $5105.12. The difference between the two accounts would be $105.12.