When Maria Acosta bought a car 2.5 years ago, she borrowed $10,000 for 48 months at 7.8% compounded monthly. Her monthly payments are $243.19, but she'd like to pay off the loan early. How much will she owe just after her payment at the 2.5 year mark? (Round your answer to the nearest cent.)
at the 2.5 year mark
i = .078/12 = ....
n = 2.5(12) = 30
follow the same steps I just showed you in your next post
Well, Maria is no stranger to car loans and monthly payments, is she? Let's crunch some numbers and find out how much she'll owe just after her payment at the 2.5 year mark.
Since she borrowed $10,000 for 48 months at 7.8% compounded monthly, her monthly payment of $243.19 is already taking that into account. It's like a magician sneaking in some interest into the loan amount.
To find out how much she'll owe just after her payment at the 2.5 year mark, we need to calculate how many payments Maria has made so far.
Since there are 12 months in a year and Maria paid for 2.5 years, that's 2.5 * 12 = 30 payments.
Now, let's calculate how much she'll owe after these 30 payments.
Using the formula for the future value of an ordinary annuity, we can do some math - or rather, let me do the math for you:
PV = PMT * (((1 + r)^n - 1) / r)
Where PV is the present value (initial loan amount), PMT is the monthly payment, r is the monthly interest rate, and n is the number of payments.
PV = $10,000
PMT = $243.19
r = 7.8% / 100 / 12 = 0.0065 (monthly interest rate)
n = 48 - 30 = 18 (remaining number of payments)
Now, let's plug in these values and calculate Maria's debt just after her payment at the 2.5 year mark:
Debt = PMT * (((1 + r)^n - 1) / r)
= $243.19 * (((1 + 0.0065)^18 - 1) / 0.0065)
And the result is... *drum roll*
Maria will owe approximately $6,726.54 just after her payment at the 2.5 year mark.
Well, that's not too bad, Maria! Keep it up, and you'll be debt-free in no time. Or maybe start a clown car business! Just a thought.
To find out how much Maria will owe just after her payment at the 2.5 year mark, we need to calculate the remaining loan balance.
First, we need to find the number of months equivalent to 2.5 years:
Number of months = 2.5 years * 12 months/year = 30 months
Next, we need to calculate the remaining loan balance using the formula for the future value of a loan:
Future Value = Present Value * (1 + r)^n - PMT * [(1 + r)^n - 1] / r
Where:
- Present Value = $10,000 (the initial loan amount)
- r = 7.8% / 12 months = 0.0065 (the monthly interest rate)
- n = 48 months (the original loan term)
- PMT = $243.19 (the monthly payment)
Now we can plug in the values into the formula:
Future Value = $10,000 * (1 + 0.0065)^30 - $243.19 * [(1 + 0.0065)^30 - 1] / 0.0065
Calculating this equation gives us the future value or remaining loan balance:
Future Value = $7,394.34
Therefore, Maria will owe approximately $7,394.34 just after her payment at the 2.5 year mark.
To find out how much Maria will owe just after her payment at the 2.5-year mark, we need to determine how many payments she has made in 2.5 years.
Since Maria borrowed the money for 48 months, the total number of payments she will make is 48.
To calculate the number of payments made up to the 2.5-year mark, we need to determine the total number of months in 2.5 years.
Since there are 12 months in a year, 2.5 years is equal to 2.5 * 12 = 30 months.
Next, we subtract the number of months Maria has paid from the total number of payments to find out how many payments she has remaining.
The remaining payments would be 48 - 30 = 18 payments.
Now we calculate how much she will owe just after her payment at the 2.5-year mark. To do this, we'll use the formula for calculating the future value of an ordinary annuity:
FV = P * (((1 + r)^n) - 1) / r
Where:
FV = Future value
P = Monthly payment
r = Monthly interest rate
n = Number of remaining payments
Plugging in the values, we get:
FV = 243.19 * (((1 + 0.078/12)^18) - 1) / (0.078/12)
Calculating this expression will give us the amount Maria will owe just after her payment at the 2.5-year mark.