Question

janissa has just purchased a new home. the house was priced at $125,000, and she chose a 40-year mortgage at 5.2%. what will her total cost be?

Answer 1

Total cost is $297148.80.

Explanation:

EMI formula is :

`(p* r*(1+r)^(n) )/((1+r)^(n) )`

p = 125000

r =
`5.2/12/100=0.00433`

t =
`40*12=480`

Putting values in formula to get her monthly payments:

`(125000*0.00433*(1+0.00433)^(480) )/((1+0.00433)^(480) )`

`(125000*0.00433*(1.00433)^(480) )/((1.00433)^(480) )`

= $619.06

Now, she will pay $619.06 per month for 40 years or 480 months.

So, total amount that will be paid by her is :

`619.06*480=297148.80`

So, total cost is $297148.80.

Answer 2

Price of the house, C = $125,000
Total number of payments, n = 40*12 = 480 months
Monthly rate, i = 5.2%/12 = 0.052/12

Monthly payment, P = C[i(1+i)^n]/[(1+i)^n-1]

Substituting;
P = 125,000[0.052/12(1+0.052/12)^480]/[(1+0.052/12)^480-1] = $619.40

Total cost = monthly payment*total number of payments = 619.40*480 = $297,312