Part V: Paying Extra

While using a $15-$year mortgage saves you money on interest compared to the

$30-$year mortgage, the monthly payment for the $15-$year loan is higher than the $30$year$.$ A good alternative is to use a $30$

year loan, but to make extra payments toward the principal. This approach gives the homeowner some flexibility

$($you can always pay the minimum monthly payment if you can't pay the extra principal$)$

$$but results in saving money on interest and paying the loan off quicker. To see the effect of making extra principal payments, you'll need some information from Part I.

Using the original loan amount

$($$$182790,30$year interest rate $(0\mathrm{.}007)$

$$and monthly payment from Part I,

$(1216\mathrm{.}11)$

$$suppose that you pay an additional $

$100$

a month toward principal. You will need to figure out how long it will take to pay off the loan with this additional payment. In order to do this, you will solve the following loan formula for N

$,$

$$which represents years:

P$0=$d$*(1(1+$r$12)12$N$)($r$12)$

Where P$0$ is the original loan amount from Part I $(182790)$and d$*$is your $30-$ year monthly payment

$(216\mathrm{.}11)$

$$plus the additional $ $100.$

$($Note: This formula shown above assumes k$=12$

$.$

$$

In order to solve the above equation for N

you would use logarithms. Using the notation log for the common logarithm, you would get the following formula:

N$=$log$(12$d$*(12$d$*$P$0$r$))(12$log$(1+$r$12))$

Use the above formula, or the original formula to solve for N

$,$

$$the number of years it will take to pay off the loan with the additional $$100$

$$payment$.$ Find N accurate to two decimal places.

N$=$Incorrect years

To find the total interest paid you need to calculate the number of payments you made. Use N

$,$

$$rounded off to two decimal places and multiplied by payments per year, $12)$

$.$

$$Then round the number of payments to the nearest whole number, since you generally make complete payments.

Total number of regular payments$=$

Now you can find the total payments and the total interest paid. Don't forget to add the additional $$100$to your monthly payment before multiplying by the number of payments.

Total payments $=$$

Total interest paid $=$$

Using the total interest paid from Part I

$(255009\mathrm{.}60)$

$,$

$$determine how much do you end up saving in interest if you pay the additional $$100$per month?

Save in interest $=$ $