Question

Lindsay is financing $350,000 to purchase a house. How much money will she save over the life of a 30-year, fixed-rate loan by buying 3 points with a rate of 6.375% instead of not buying points with a rate of 6.75%?

Answer 1

$2,596.50

$13,096.50

$20,658.00

$31,158.00

Answer 2

@jim_thompson5910

Answer 3

We'll use an amortization schedule which is typically worked out taking the principal left at the end of each month, multiplying by the monthly rate and then subtracting the monthly payment. This is typically generated by an amortization calculator using the following formula:

$$
\large{
A =P\cdot\frac{r(1 + r)^n}{(1 + r)^n - 1}\
}
$$

A is the periodic amortization payment (i.e.monthly payment)
P is the principal amount borrowed
r is the percentage rate per period; for a monthly payment, take the Annual Percentage Rate (APR)/12
n is the number of payments; for monthly payments over 30 years, 12 months x 30 years = 360 payments.


Using 6.375%

$$
\large{
A_{6.375} =350000\cdot\frac{(.06375/12)(1 + (.06375/12))^{12*30}}{(1 + (.06375/12))^{12*30} - 1}\
}
$$

Using 6.75%

$$
\large{
A_{6.75} =350000\cdot\frac{(.0675/12)(1 + (.0675/12))^{12*30}}{(1 + (.0675/12))^{12*30} - 1}\
}
$$

Total savings (S) over lifetime would be:
$$
\large{
S=A_{6.75}*30\times12 -A_{6.375}*30\times12\\
=30\times12(A_{6.75}-A_{6.375})
}
$$

That's it!.

Answer 4

what does the answer come out to be

Answer 5

@ybarrap

Answer 6

$$
\large
A_{6.375}=$2,183.54
$$
$$
\large
A_{6.75}=$2270.09
$$
So,
$$
\large
S=30\times12(2,270.09-2,183.54)=$31,158.00
$$

Make sense?

Answer 7

yes it does . thank u so much