Welcome!
In this video, I’m going to use the BAii plus calculator to solve this amortization
problem.
A $450,000 mortgage loan, financed at 2.8% compounded semi-annually, requires month-end
payments of $1850.
How many payments are required?
To solve this, let’s first set P/Y to 12 (since payments are made monthly) and then
we set C/Y to 2 for semiannual compounding.
Press 2nd Quit.
Next input 2.8 I/Y for interest, 450,000 for Present Value,
1850 (negative) for payments (since payment is an outflow),
and then 0 Future value since we plan to pay off the mortgage at the end.
And when we compute N, we obtain 358.53.
That is, 359 payments are required.
The size of the 359th payment however will be smaller than the previous payments of 1850.
To find the principal repaid in the 10th payment, we press 2nd AMORT,
set P1 to 10, ENTER, scroll down, set P2 to 10 as well, ENTER
and when you scroll down, you see the outstanding balance after the 10th payment, when you scroll
down again, you see the principal repaid in the 10th payment which is 823.06.
Next we want to calculate the total interest paid in the 2nd year.
Since payments are made monthly, the first year comprises of payments 1 to 12.
The second year will comprise of the next 12 payments which will be 13th to the 24th.
So we set P1 to 13 ENTER, scroll down, and set P2 to 24 ENTER.
Scroll down to interest, and we have a total interest of $12,126.51 for the second year.
Next we want to calculate the outstanding principal balance at the end of the first
four years.
Since payments are made monthly, in four years we have 4 times 12 which equals 48 payments.
So 2nd AMORT, P1 can be any value less than 48 but we want to be sure we set P2 to 48
ENTER.
And when we scroll down we see that the balance is 409122.15.
To find the total interest paid in the first 5 years, we set P1 to 1,
scroll down and set P2 to 5 time 12 which equals 60.
ENTER then scroll down to INTEREST and we have 59,172.31.
Next we find the size of the final payment.
Recall that N equals 358.53, So the final payment is the 359th payment.
So we set P1 and P2 to 359.
And we can see here that the outstanding balance is 870.25 which actually represents an overpayment
if we make the regular payment of 1850.
So to find the required last payment, we subtract the overpayment value of 870.25 from the regular
payment of 1850, and that gives 979.75.
So the size of the las payment is 979.75.
And that’s it for this video.
Thanks for watching.