Question

Joe Levi bought a home in Arlington, Texas, for $147,000. 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%

Answer 1

Answer:

53,367

Explanation:

The first thing we do is to substract the down payment from the initial amount, because this payment is not part of the mortgage.

147,000 x 25% = 36,750

147,000 - 36,750 = 110,250

Next, to find the financed amount we use the present value of an annuity formula:

PV = X [(1 - (1 + i)^-n) / i ]

Where:

• PV = Present value, in this case, the initial financed amount of $110,250
• X = Value of the annuity payments.
• i = Interest rate
• n = number of compounding periods

For the 8% interest rate we have:

110,250 = X [(1 - (1 + 0.08)^-30) / 0.08]

110,250 = X [11.26]

110,250 / 11.26 = X

9,791.3 = X

Now we multiply this value by 30 to obtain the total amount paid

9,791.3 * 30 = 293,739

The total interest cost under then 8% interest rate is the total amound paid minus the initial amount:

Total interest cost = 293,739 - 110,250

                              = 183,489

We do the same for the 6% interest rate:

110,250 = X [(1-(1 + 0.06)^-30) / 0.06]

110,250 = X [13.76]

110,250 / 13.76 = X

8,012.4 = X

8,012.4 * 30 = 240,372

Total interest cost = 240,372 - 110,250

                              = 130,122

Difference in interest cost = 183,489 - 130,122

                                           = 53,367