You just move into your new home for which you have a 30 year mortagage of $60,000 at 7%. Your new neighbor Jack tells you that if you double the amount of your payment each month you will cut the length of time you pay in half. Is he correct? would the payoff period be longer or shoter than 1/2 the 30 year payoff time?
To determine if Jack's claim is correct, we need to calculate the payoff periods for both the regular payment schedule and the doubled payment schedule.
Let's start with the regular payment schedule. You have a 30-year mortgage of $60,000 at 7% interest. To calculate your monthly payment, you can use the standard formula for a fixed-rate mortgage:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]
Where:
M = Monthly payment
P = Principal amount (loan amount)
i = Monthly interest rate (annual rate divided by 12)
n = Total number of payments (number of years multiplied by 12)
For your mortgage:
P = $60,000
i = 7% / 12 = 0.07 / 12 = 0.00583 (monthly interest rate)
n = 30 years * 12 = 360 months
Using these values, we can calculate the monthly payment:
M = 60000 * [ 0.00583(1 + 0.00583)^360 ] / [ (1 + 0.00583)^360 - 1 ]
M ≈ $399.18 (rounded to the nearest cent)
Therefore, your regular monthly payment will be approximately $399.18.
Now, for the doubled payment schedule, you would need to double the amount of your monthly payment each month. Assuming you start with the regular monthly payment of $399.18, the payment for the second month would be $399.18 * 2 = $798.36, the payment for the third month would be $798.36 * 2 = $1596.72, and so on.
To calculate the payoff period for the doubled payment schedule, we can sum up the payment amounts until the total exceeds the mortgage amount ($60,000).
By calculating the total payment amounts over time, we find that the payoff period for the doubled payment schedule is approximately 14 years and 11 months.
Comparing this to the original 30-year mortgage term, we can see that Jack's claim is correct. The payoff period for the doubled payment schedule is indeed shorter than half the 30-year payoff time.
Therefore, if you double the amount of your payment each month, you can cut the length of time you pay in half, achieving a payoff period of approximately 14 years and 11 months.