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?

give it a shot, it is simply a lot of button-pushing.

To calculate the amount of John's payment over the life of his adjustable-rate mortgage, we need to determine the annual payment for each year and add them up.

First, let's calculate the annual payment for each year based on the outstanding loan balance and the interest rate for that year.

In Year 1, the mortgage balance is $150,000, and the interest rate is 6%. So, the annual payment for Year 1 can be calculated using the formula for a mortgage payment:

Annual payment = Mortgage balance * (Interest rate / (1 - (1 + Interest rate)^(-Number of years)))

Annual payment = $150,000 * (0.06 / (1 - (1 + 0.06)^(-5)))

Using a financial calculator or spreadsheet, we find that the annual payment for Year 1 is approximately $35,739.

Similarly, we can calculate the annual payments for Years 2 to 5 using the same formula but with the respective interest rates for each year.

Year 2: Annual payment = $150,000 * (0.07 / (1 - (1 + 0.07)^(-4)))
Year 3: Annual payment = $150,000 * (0.08 / (1 - (1 + 0.08)^(-3)))
Year 4: Annual payment = $150,000 * (0.09 / (1 - (1 + 0.09)^(-2)))
Year 5: Annual payment = $150,000 * (0.1 / (1 - (1 + 0.1)^(-1)))

Using a financial calculator or spreadsheet, we find the annual payments for Years 2 to 5 to be approximately $37,868, $40,839, $44,959, and $50,455, respectively.

To calculate the total payment over the life of the adjustable-rate mortgage, we add up the annual payments for all five years:

Total payment = Year 1 payment + Year 2 payment + Year 3 payment + Year 4 payment + Year 5 payment

Total payment = $35,739 + $37,868 + $40,839 + $44,959 + $50,455

Total payment = $210,860

Now, let's compare these findings to if John had taken out a fixed-rate loan for the same period at 7.5%.

To calculate the annual payment for a fixed-rate loan, we use the same formula as above, but with the fixed interest rate of 7.5% throughout all five years:

Annual payment = $150,000 * (0.075 / (1 - (1 + 0.075)^(-5)))

Using a financial calculator or spreadsheet, we find the annual payment for the fixed-rate loan to be approximately $37,696.

Since the fixed-rate loan has a constant interest rate over the five years, the total payment over the life of the loan would simply be the annual payment multiplied by the number of years:

Total payment = Annual payment * Number of years

Total payment = $37,696 * 5

Total payment = $188,480

Comparing the two findings, we see that the total payment over the life of the adjustable-rate mortgage is $210,860, while the total payment for the fixed-rate loan is $188,480.

Therefore, in this scenario, taking out the fixed-rate loan at 7.5% would be the better deal for John, as it would result in lower total payments over the life of the loan.