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
