Shawna wants to buy a new car that costs $25 000. She is given a loan from the bank that has an interest rate of 8.5% per year compounded monthly. Shawna wants to have this loan paid off in 4 years. What is her monthly payment?
To calculate Shawna's monthly payment, we need to use the formula for calculating the monthly payment on a loan:
\[ P = \frac{r(PV)}{1-(1+r)^{-n}} \]
Where:
P = monthly payment
r = monthly interest rate (annual interest rate divided by 12)
PV = present value or loan amount
n = total number of payments
First, we need to convert the annual interest rate to a monthly interest rate. Since the interest is compounded monthly, we divide the annual interest rate by 12 and convert it to a decimal:
\[ r = \frac{8.5}{100} ÷ 12 = 0.0071 \]
Next, we need to calculate the total number of payments:
\[ n = 4 \times 12 = 48 \]
Finally, we can substitute the values into the formula:
\[ P = \frac{0.0071(25000)}{1-(1+0.0071)^{-48}} \]
Calculating this expression will give us Shawna's monthly payment.
To calculate Shawna's monthly payment, we can use the formula for calculating the monthly payment on a loan.
The formula for calculating the monthly payment on a loan is:
P = (r * PV) / (1 - (1 + r) ^ -n)
Where:
P = Monthly Payment
r = Monthly interest rate
PV = Present value or loan amount
n = Number of monthly payments
In this case, Shawna wants to borrow $25,000, the interest rate is 8.5% per year compounded monthly, and she wants to pay off the loan in 4 years (48 months).
First, we need to convert the annual interest rate to a monthly rate:
Monthly interest rate = Annual interest rate / Number of months in a year
Monthly interest rate = 8.5% / 12 = 0.085 / 12 = 0.00708333
Now, we can substitute the values into the formula and calculate Shawna's monthly payment:
P = (r * PV) / (1 - (1 + r) ^ -n)
P = (0.00708333 * $25,000) / (1 - (1 + 0.00708333) ^ -48)
P ≈ $603.02
Therefore, Shawna's monthly payment will be approximately $603.02.