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
Kevin's Account:
Pt = Po + Po*r*t.
Pt = 4000 + 4000*0.05*5 = $5000.
Jill's Account:
Pt = Po(1+r)^n.
r = 5%/100% = 0.05 = APR expressed as a decimal.
n = 1comp/yr * 5yrs = 5 Compounding
periods.
Pt = 4000(1.05)^5 = $5105.13.
Diff. = 5105.13 - 5000 = $105.13.
To calculate the balance of Kevin's account after 5 years with 5% simple interest, you can use the formula:
Balance = Principal + (Principal * Interest Rate * Time)
In this case, the principal (initial deposit) is $4000, the interest rate is 5% (0.05), and the time is 5 years. Plugging these values into the formula, we get:
Kevin's Balance = $4000 + ($4000 * 0.05 * 5)
= $4000 + ($1000)
= $5000
Therefore, Kevin's account balance at the end of 5 years would be $5000.
To calculate the balance of Jill's account after 5 years with 5% interest compounded annually, you can use the formula for compound interest:
Balance = Principal * (1 + Interest Rate)^Time
In this case, the principal is $4000, the interest rate is 5% (0.05), and the time is 5 years. Plugging these values into the formula, we get:
Jill's Balance = $4000 * (1 + 0.05)^5
= $4000 * (1.05)^5
≈ $5448.63
Therefore, Jill's account balance at the end of 5 years would be approximately $5448.63.
To calculate the difference between each account, subtract Kevin's balance from Jill's balance:
Difference = Jill's Balance - Kevin's Balance
= $5448.63 - $5000
≈ $448.63
Therefore, the difference between each account balance would be approximately $448.63.