Question

Paul will be able to save $513 per month(which xan be used for mortagage payments) for the indefinite future. If Paul finances the remaining costs of a $134,000 home, after making a $26,800 down payment,(amount to finance $107,200) at a rate of 5% over 30 years, what are his resulting monthly mortgage payments? Can he afford the Mortgage?

Answer 1

Total amount financed = $107200

For calculating the monthly payments on financed amount, we will use the present value of annuity formula as below:

Here, the payments will be same every month, so it is an annuity. For calculating the present value of annuity, we will use the following formula:

PVA = P * (1 - (1 + r)-n / r)

where, PVA = Present value of annuity = $107200, P is the periodical amount , r is the rate of interest = 5%. Monthly rate = 5% / 12 = 0.416667% and n is the time period = 30 * 12 = 360 months

Now, putting these values in the above formula, we get,

$107200 = P * (1 - (1 + 0.41667%)-360 / 0.416667%)

$107200 = P * (1 - ( 1+ 0.00416667)-360 / 0.00416667)

$107200 = P * (1 - ( 1.00416667)-360 / 0.00416667)

$107200 = P * (1 - 0.22382656889) / 0.00416667)

$107200 = P * (0.77617343111 / 0.00416667)

$107200 = P * 186.2814744

P = $107200 / 186.281474412204

P = $575.47

So, monthly payments are $575.47

Since monthly payments are more than the actual savings of $513, so he cannot afford the mortgage.