monthly payment

Question

Am ice cream store sells for $125000 and a $40000 down payment is made. A 25-year mortgage at 7.5 is obtained. Find the monthly payment?

Answer 1

This is an economics problem

 

First, with a down payment of $40,000, what remains to be paid is 125000-40000=$85,000 over a 25 year period with an apr of 25%

 

hence we have to calculate the monthly payment at a monthly rate of 7.5/12 % = 0.625% or 5/8%

 

Method 1

 

Use the equation for capital recovery factor   CRF = i(1+i)ⁿ/((1+i)ⁿ - 1)

 

putting i = 0.625% = 0.00625, and n = 300 months, the CRF = 0.0074

 

Hence monthly payment = 85,000 * 0.0074 = $628 per month

 

Method 2 

 

you can go online (google.com) and find annuity tables; there are about 8 columns, the column you are interested in is capital recovery factor or Annuity given Principal or A/P

 

You will have to do a bit of interpolation as 5/8 does not appear in the table but 1/2 and 3/4 appear, hence 5/8 would be midway between the two. Also in 25 years = 25*12 = 300 months; in the tables 240, and 360 occurs, 300 happens to be the midpoint, from that interpolation (A/P, 5/8, 300) = 0.0075

 

Hence the monthly payment is, $85,000 * 0.0075 =  $638 per month (which is close to the value from method 1).