Question

You buy a new home for $500,000 on the first day of the month. You put down $50,000 and finance the rest with a mortgage at 6% annual interest compounded monthly on the last day of the month. Your monthly payments including principal and interest are 2500. Your payments are due on the first day of the month, starting next month. What is your loan balance after your third monthly payment ? explain how you got the answer !

Answer 1

First Method

Loan amount=500000-50000=$45000

Rate of interest=i=6%/12=0.5% per month

Interest for first installment=450000*0.5%=$2250

Amount due after 1st month=450000+2250=$452250

Balance due after 1st installment=452250-2500=$449750

Interest for second installment=449750*0.5%=$2248.75

Amount due after 2nd month=449750+2248.75=$451998.75

Balance due after 2nd installment=451998.75-2500=$449498.75

Interest for third installment=449498.75*0.5%=$2247.49

Amount due after 3rd month=449498.75+2247.49=$451746.24

Balance due after 3rd installment=451746.24-2500=$449246.24

With this method, we can calculate for small number of periods but it becomes very lengthy if period of payment is long. So, we can go for formula.

Second method

Balance due after 3rd installment=450000*(F/P,0.5%,3)-2500*(F/A,0.5%,3)

Let us calculate interest factors

(F/P,0.005,3)=(1+0.005)³=1.015075

(FA, i, n) = (1+i)"一1

(F/A,0.005, 3) (1 +0.005)3-1 ,005 3.015025

Balance due after 3rd installment=450000*1.015075-2500*3.015205=$449246.24