Question

Many mortgage company allow you to "buy down" your interest rate of your loan by buying points. A point is equal to 1% of your mortgage amount (or $1,000 for every $100,000). You're essentially paying some interest up front in exchange for a lower interest rate over the life of your loan. Find the following payments and total cost (including points) of a $219,000.00 that is borrowed for 30 years with a) 7 1 2 % compounded monthly with no points $ . The total cost would be $ b) 7 1 4 % compounded monthly with 1 point $ . The total cost would be $

Answer 1

The monthly payments and the total costs are

• $1,531.29 and $551264.40
• $1,531.29 and $1339664.40

How to determine the payments and the total cost

a) 7 1/2 % compounded monthly with no points

Here, we have

The monthly interest rate is 7.5%/12 = 0.625%.

The number of monthly payments is 30 years * 12 months/year = 360 months.

So, the monthly payment can be calculated using the formula:

`M = (P[i(1 + i)^n])/((1 + i)^n - 1)`

Where:

• M is the monthly payment
• P is the principal amount ($219,000.00)
• i is the monthly interest rate (0.625%)
• n is the number of payments (360)

Substitute the known values into the equation

`M = (219000 * [0.00625 * (1 + 0.00625)^(360)])/((1 + 0.00625)^(360) - 1)`

M = $1,531.29

For the total cost, we have

Total cost = $1,531.29/month * 360 months

Total cost = $551264.40

b) 7 1/4 % compounded monthly with 1 point

Here, we have

One point is equal to 1% of the mortgage amount, so buying one point would cost $2,190.00.

The other parameters remain the same

So:

`M = (219000 * [0.00625 * (1 + 0.00625)^(360)])/((1 + 0.00625)^(360) - 1)`

M = $1,531.29

For the total cost, we have

Total cost = ($1,531.29 + $2190.00)/month * 360 months

Total cost = $1339664.40