Question

4. Joe Levi bought a home in Arlington, Texas, for $127,000. He put down 25% and obtained a mortgage for 30 years at 8.00%. What is the difference in interest cost if he had obtained a mortgage rate of 6.00%? (Use Table 15.1.) (Use 360 days a year. Round your intermediate values and final answer to the nearest cent.) Difference $

Answer 1

Step-1:

Calculation of Interest costs at 8%

a.

Monthly Payment

$           699.18

Working:

i.

Present Value of annuity of 1

=

(1-(1+i)^-n)/i

Where,

=

(1-(1+0.00667)^-360)/0.00667

i

8%/12

=

0.00667

=

136.2317

n

30*12

=

360

ii.

Cost of house

$       1,27,000

Down Payment

$           31,750

Mortgage amount

$           95,250

iii.

Monthly Payment

=

Mortgage Amount/Present value of annuity of 1

=

$           95,250

/

136.2317

=

$           699.18

b.

Total Interest costs

$ 1,56,453.50

Working:

Total Payment

=

$           699.18

x

360

=

$ 2,51,703.50

Mortagage Amount

$           95,250

Total Interest Costs

$ 1,56,453.50

Step-2:

Calculation of Interest costs at 6%

a.

Monthly Payment

$           571.07

Working:

i.

Present Value of annuity of 1

=

(1-(1+i)^-n)/i

Where,

=

(1-(1+0.005)^-360)/0.005

i

6%/12

=

0.005

=

166.7916

n

30*12

=

360

ii.

Cost of house

$       1,27,000

Down Payment

$           31,750

Mortgage amount

$           95,250

iii.

Monthly Payment

=

Mortgage Amount/Present value of annuity of 1

=

$           95,250

/

166.7916

=

$           571.07

b.

Total Interest costs

$ 1,10,335.88

Working:

Total Payment

=

$           571.07

x

360

=

$ 2,05,585.88

Mortagage Amount

$           95,250

Total Interest Costs

$ 1,10,335.88

Step-3:Calculate difference in Interest Costs

Interest Costs at 8%

$ 1,56,453.50

Interest Costs at 6%

$ 1,10,335.88

Difference in interest costs

$     46,117.62