# The price of a small cabin is \$45,000. The bank requires a 5% down payment. The buyer is offered two mortgage options: 20-year fixed at 8% or 30 year fixed at 8%. Calculate the amount of interest paid for each option. And how much does the buyer save in interest with the 20-year option? Care not to combine too many questions into one as the eNotes rules do not allow it. I will answer accordingly and you will be able to calculate any remaining answers from the information given below:

First we will have to calculate the monthly repayment. You have not said that interest is compounded monthly but I have assumed as it is usual for a mortgage bond.

```P_(v) = (x[1-(1+i)^(-n)])/ i`

We use the present value formula because we know how much money he has NOW. Take 5% of \$45 000= \$2250

Thus we must borrow \$42 750 and the interest rate is 8%= 0.08. We compound monthly so divide the interest by 12 `0.08/12`

`therefore P_(v) = 42 750`

`x= unknown`

`i = 0.08/12`

`n= 20 times 12`  or for the 30 year term `n=30 times 12`

Now substitute into the formula:

`42750 = (x[1-(1+0.08/12)^(-20 times 12)])/(0.08/12)`

CARE not to round off your answers too soon. Plug values into your calculator and only round off at the end! Obviously I will have to show some rounded off values for the purposes of this example:

20 years: `42750 times (0.08/12)= x[1-(1.0066667)^(-240)]`

30 years:`42750 times(0.08/12)=x[1-(1.0066667)^(-360)]`

20years: `285 = x(0.797028611)`

30 years: `285= x(0.908556736)`

20years: `therefore x= 285/0.797028611= 357, 58`

30 years : `therefore x = 285/0.908556736= 313,68`

So over 20 years \$357 x 240 months = \$85 819,20

and over 30 years \$313,68x 360 months=\$112 926,35

`therefore` the interest over 20 years or 30 years is the total minus the capital amount of \$42 750

Interest over 20 years = 85 819,20 - 42 750 = \$43 069, 20

Interest over 30 years= 112 926,35- 42750= \$70 176,35

Approved by eNotes Editorial Team