To help pay for art school Keith borrowed money from an online lending company he took out a personal amortized loan for $50,000 at an interest rate of 5.7% with monthly payments for a term of 20 years for each part do not round any intermediate computations and round your final answers to the nearest cent find Keith's monthly payment
To find Keith's monthly payment, we can use the formula for calculating the fixed monthly payment for an amortized loan:
P = (r * PV) / (1 - (1 + r)^(-n))
Where:
P = Monthly payment
r = Monthly interest rate
PV = Present value (loan amount)
n = Total number of monthly payments
First, we need to calculate the monthly interest rate:
r = 5.7% / 100 / 12
r = 0.057 / 12
r = 0.00475
Next, we substitute the given values into the formula:
P = (0.00475 * $50,000) / (1 - (1 + 0.00475)^(-20*12))
Calculating the exponent:
1 + 0.00475 = 1.00475
-20 * 12 = -240
P = (0.00475 * $50,000) / (1 - 1.00475^-240)
Using a calculator, we find:
P ≈ $346.12
Therefore, Keith's monthly payment is approximately $346.12.
To find Keith's monthly payment, we can use the amortization formula:
Monthly Payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1),
where:
P = loan amount (principal)
r = monthly interest rate
n = number of monthly payments
Given:
P = $50,000
r = 5.7% / 100 (converted to decimal)
n = 20 years * 12 months/year
Let's calculate:
r = 5.7% / 100 = 0.057
n = 20 * 12 = 240
Plugging in the values into the formula:
Monthly Payment = $50,000 * (0.057 * (1 + 0.057)^240) / ((1 + 0.057)^240 - 1)
Calculating this equation will give Keith's monthly payment.