Henry Ford College purchased a commercial building for 3 400

Henry Ford College purchased a commercial building for $3, 400,000.00 to use as a new student center. HFC pays $30% down and finance the balance at 6 1/2 % for 25 years. Real estate taxes are $9, 600 per year and insurance is $3,000 per year. Dearborn guarantees HFC that neither will increase during this 25 year period. Determine: a) the total monthly payment including taxes and insurance; and b) the total cost of owning the building (for 25 years) including the down payment.

Solution

Cost of the building = 3.4* 10⁶ = 3.4 million; 30% was down payment = 1.02 million
Hence rest 3.4-1.02= 2.38 million in down payment at 6.5% for 25 years;
Yearly tax = 9,600 and yearly insurance = 3000; Yearly taxes + insurance = 12,600;
Monthly taxes + insurance = 12600/12= 1,050;
EMI for balance 2.38 million is given by the formula =
P*r* (1+r)ⁿ / (1+r)ⁿ -1;
Here P = principal amount = 2.38 * 10⁶ ;
n = number of payments = 25*12 = 300
r= interest rate for each payment = 6.5/12= 0.5417%
Substituting values we get
= 2.38*10⁶ * 0.005417* (1.005417)³⁰⁰ / (1.005417³⁰⁰ -1) = 16,071 $
So EMI + insruance and taxes = 16,071+ 1050 = 17,121 $

Thus monthly amount including taxes and insurance = 17,121$

Total cost of owning the building = down payment + cummulative sum of monthly payments for 25 years
= 1.02 million + 17121*300=1020000 + 5136300 = 6156300