Question

Forty-eight (48) months ago, James Alfred Charles purchased a $2,750,000 house in Buckhead with no money down (i.e. he borrowed $2,750,000). The interest rate on his 30-year, monthly payment loan was 6.25 percent. For the first 48 months of the loan, James paid twice the normal required payment (for example, if the required payment to pay off the loan in 30 years was $4000 per month, James actually paid $8000 per month, with all excess being applied against the principle balance).

Now, James is thinking about downsizing and he would like to know how much equity he has accumulated in his home. Unfortunately, the market value of his home has depreciated by 30 percent over the past 4 years (thus, James can only sell his house today for $1,925,000).

Assuming that James made all of his monthly payments (i.e., twice the required amount) on time and assuming that he can sell his house today (i.e., immediately after making his 48th monthly payment) for $1,925,000, how much equity can James Alfred Charles expect to take out of his home? (Note: for this problem, to achieve as precise an answer as possible, round all intermediate calculations – payment, interest rate, N, etc. to a minimum of 4 decimal places).

Answer 1

Step 1: Compute the normal required payment
PV=-2750000
N=12*30
I/Y=6.25%/12
FV=0
CPT PMT=$16,932.22

Step 2: Compute the loan outstanding after 48 months
PMT=16932.22*2
PV=-2750000
I/Y=6.25%/12
N=48
CPT FV=-$1,687,469.07

Equity=1925000-1687469.07=$237,530.93