Oprah Winfrey has closed on a 42-acre estate near Santa Barbara, California, for $50,000,000. If Oprah puts 20% down and finances at 7% for 30 years, what would her monthly payment be?

Steve wrote a nice solution several years back...

M = Pr/(1-(1+r)^-n)

= 40,000,000*(.07/12)/(1-(1+.07/12)^(-12*30))
= 266121

LOL! Someone asked this same question yesterday... but did not respond when I asked what is the compounding of the loan??

It was me, I am sorry I did not see what you posted. This problem is related to PMT and then you're supposed to find interest with P1 and P2.

I will assume the compounding is monthly to match the payment period, or else we have a messy solution

i = .07/12 = .00583333...
n = 360

paym(1 - 1.0058333..^-360)/.00583333... = .8(50000000)

To calculate the monthly payment for Oprah Winfrey's loan, we first need to determine the loan amount and then use an amortization formula. Here are the steps to find the answer:

Step 1: Calculate the loan amount
Oprah put 20% down on the estate, so the loan amount would be 80% of the purchase price. We can calculate it as follows:
Loan Amount = Purchase Price * Down Payment Percentage
Loan Amount = $50,000,000 * 0.80
Loan Amount = $40,000,000

Step 2: Calculate the monthly interest rate
Given that the financing is at 7% for 30 years, we need to convert the annual interest rate to a monthly rate. To do this, we divide the annual rate by 12 (number of months):
Monthly Interest Rate = Annual Interest Rate / 12
Monthly Interest Rate = 7% / 12
Monthly Interest Rate = 0.07 / 12
Monthly Interest Rate = 0.00583 (rounded to 5 decimal places)

Step 3: Calculate the number of monthly payments
Since the financing term is for 30 years, we need to multiply the number of years by 12 (number of months):
Number of Monthly Payments = Number of Years * 12
Number of Monthly Payments = 30 * 12
Number of Monthly Payments = 360

Step 4: Calculate the monthly payment using the loan amount, interest rate, and number of payments
To calculate the monthly payment, we can use the following formula:

Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Monthly Payments))

Using the loan amount, monthly interest rate, and number of monthly payments calculated earlier, we can substitute these values into the formula to find the monthly payment.

Monthly Payment = ($40,000,000 * 0.00583) / (1 - (1 + 0.00583)^(-360))

Now, we can calculate the value of the expression:

Monthly Payment ≈ $239,739.64 (rounded to the nearest cent)

Therefore, Oprah Winfrey's monthly payment would be approximately $239,739.64 if she financed $40,000,000 at 7% for 30 years with a 20% down payment.