A person wishes to borrow $20,000 and has the following options. One lending source offers the loan for 24 monthly payments at an annual percentage rate of 14%. The second source offers the loan for 18 monthly payments at an annual percentage rate of 16% which of these two payment schedules has the lower monthly payment
Plug and chug:
M = Pr/(1-(1+r)^-n)
To determine which payment schedule has the lower monthly payment, we can calculate the monthly payments for both options and compare them.
First, let's calculate the monthly payment for the loan from the first lending source. We can use the formula for a fixed-rate loan payment:
Monthly payment = P * (r(1+r)^n) / ((1+r)^n-1)
Where:
P = Loan amount ($20,000)
r = Monthly interest rate (annual percentage rate / 12) = 14% / 12 = 0.14 / 12
n = Number of monthly payments (24)
So, for the first lending source, the monthly payment would be:
Monthly payment = 20,000 * (0.14/12 * (1+0.14/12)^24) / ((1+0.14/12)^24-1)
Next, let's calculate the monthly payment for the loan from the second lending source. Using the same formula:
P = Loan amount ($20,000)
r = Monthly interest rate (annual percentage rate / 12) = 16% / 12 = 0.16 / 12
n = Number of monthly payments (18)
So, for the second lending source, the monthly payment would be:
Monthly payment = 20,000 * (0.16/12 * (1+0.16/12)^18) / ((1+0.16/12)^18-1)
After calculating both monthly payments, you can compare them to determine which payment schedule has the lower monthly payment. Choose the option with the lower monthly payment to make it more affordable for the borrower.