Consider the following scenario: John buys a house for $150,000 and takes out a five year adjustable rate mortgage with a beginning rate of 6%. He makes annual payments rather than monthly payments.

Unfortunately for John, interest rates go up by 1% for each of the five years of his loan (Year 1 is 6%, Year 2 is 7%, Year 3 is 8%, Year 4 is 9%, Year 5 is 10%).
Calculate the amount of John's payment over the life of his loan. Compare these findings if he would have taken out a fix rate loan for the same period at 7.5%. Which do you think is the better deal?

When I answered this identical post for you yesterday, I was hoping you would make an attempt.

http://www.jiskha.com/display.cgi?id=1287786024

It is not that hard.
let the annual payment be x

then
x(1.06)^-1 + x(1.07)^-2 + ... + x(1.10)^-5 = 150000
take out x as a common factor to have

x(1.06)^-1 + 1.07^-2 + ... + 1.10^-5) = 150000

x = .... You do the button-pushing

vs

x( 1 - 1.075^-5)/.075 = 150 000
I had calculated that for you in an earlier post when you asked for the chart.

To calculate the amount of John's payment over the life of his loan, we need to calculate the annual payment for each year and then sum them up.

Let's start with the adjustable rate mortgage. Since John took out a five-year adjustable rate mortgage with a beginning rate of 6%, his annual payments for each year can be calculated using the formula:

Payment = Loan amount * Interest rate

Year 1 payment = $150,000 * 6% = $9,000
Year 2 payment = $150,000 * 7% = $10,500
Year 3 payment = $150,000 * 8% = $12,000
Year 4 payment = $150,000 * 9% = $13,500
Year 5 payment = $150,000 * 10% = $15,000

Now, let's calculate the total amount John would pay over the life of his loan:

Total payment = Year 1 payment + Year 2 payment + Year 3 payment + Year 4 payment + Year 5 payment
= $9,000 + $10,500 + $12,000 + $13,500 + $15,000
= $60,000

Now let's compare this to the fixed rate loan calculation. If John had taken out a fixed rate loan for the same period at 7.5%, his annual payment for each year would be:

Year 1 payment = $150,000 * 7.5% = $11,250
Year 2 payment = $150,000 * 7.5% = $11,250
Year 3 payment = $150,000 * 7.5% = $11,250
Year 4 payment = $150,000 * 7.5% = $11,250
Year 5 payment = $150,000 * 7.5% = $11,250

Total payment = Year 1 payment + Year 2 payment + Year 3 payment + Year 4 payment + Year 5 payment
= $11,250 + $11,250 + $11,250 + $11,250 + $11,250
= $56,250

Comparing the two calculations, we find that John would pay a total of $60,000 over the life of the adjustable rate mortgage and a total of $56,250 over the life of the fixed rate loan.

Based on these findings, the fixed rate loan at 7.5% would be the better deal for John. It would result in lower total payments over the life of the loan compared to the adjustable rate mortgage.