The total lifetime cost for Miranda to pay off her 4 loans is $177,768.00.
Step 1: Calculate the monthly payment for each loan
We can use the formula for the monthly payment of a loan to calculate the monthly payment for each of Miranda's loans. The formula is:
M = P * (i(1 + i)^n) / ((1 + i)^n - 1)
where:
M is the monthly payment
P is the principal amount of the loan
i is the monthly interest rate
n is the total number of payments
In this case, the principal amount is $6,500, the monthly interest rate is 7.5% / 12 = 0.625%, and the total number of payments is 10 years * 12 months/year = 120 months.
Plugging these values into the formula, we get:
M = 6500 * (0.00625(1 + 0.00625)^120) / ((1 + 0.00625)^120 - 1)
M = 370.35
Therefore, the monthly payment for each loan is $370.35.
Step 2: Calculate the total lifetime cost for all 4 loans
The total lifetime cost for Miranda to pay off her 4 loans is simply the sum of the monthly payments for all 4 loans. The monthly payment for each loan is $370.35, so the total monthly payment for all 4 loans is 4 * $370.35 = $1481.40.
The total lifetime cost for Miranda to pay off her 4 loans is therefore $1481.40 * 120 months = $177,768.
Step 3: Round the total lifetime cost to the nearest cent
The total lifetime cost of $177,768.00 should be rounded to the nearest cent, which is $177,768.00.
Therefore, the total lifetime cost for Miranda to pay off her 4 loans is $177,768.00.