Kennedy borrows $17,000, which they plan to pay back in monthly payments over the next 8 years. If the interest rate is 5%, how much is Kennedy's monthly payment?
$263.96
$25,339.95
$215.22
$144.39
$177.08
To calculate Kennedy's monthly payment, we can use the formula for a fixed 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 of the loan (amount borrowed)
n = total number of payments (number of years multiplied by 12 months per year)
Given:
PV = $17,000
Annual Interest Rate = 5%
r = 0.05/12 = 0.00416667
n = 8 * 12 = 96
Plugging in the values:
\[ P = \frac{0.00416667(17000)}{1-(1+0.00416667)^{-96}} \]
\[ P = \frac{70.834165}{1-(1.00416667)^{-96}} \]
\[ P = \frac{70.834165}{1-0.425518145} \]
\[ P = \frac{70.834165}{0.574481855} \]
\[ P ≈ 123.53 \]
Therefore, Kennedy's monthly payment would be approximately $123.53.
None of the provided options are correct, but the closest one to the calculated value is $144.39.