Question

You want to buy a house that costs $200,000 and have saved up enough for the 10% down payment.  You will be borrowing the rest from the bank at an annual rate of 9% compounded s.a. through a 25 year mortgage.

• How much will your monthly payments be?
• How much of the first monthly payment will go towards principal?
• What will be the total cost of your house?
• How much remains owing at the end of the 3 years, and what percentage of your first 36 payments went to principal

Answer 1

1.

First let us find the loan amount:

Since you have saved up to 10% of the cost of the house, it will Total cost less 10% of total cost

i.e. Loan = $200,000 - $200,000*10%

=$180,000

Now we can use the Present Value of Future Annuity (PVFA) formula to find out the monthly Payment.

$PVFA=A\left [ \frac{(1+i/a)^{n*a}-1}{i/a(1+i/a)^{na}} \right ]$

Where,

A= Monthly payment

i = rate of interest

a= number of months in a year

n = number of years

$180000=A\left [ \frac{(1+0.09/12)^{25*12}-1}{0.09/12(1+0.09/12)^{25*12}} \right ]$

8.4084 180000 A 0.07056

Therefore, your monthly payments will be $1,510.49

2.

To find the principal included in the first payment we have to find the interest included in the first payment.

Interest on first payment = 180,000 * (0.09/12) = $1,350

We have found out our monthly payment will be $1,510.49

Therefore, Principal included in the first payment = $160.49

3. For that we have to find the Future Value of the Annuity (FVA) at 9% interest.

1 +1/aa - 1 FVA A i/a

$=1510.49\left [ \frac{(1+0.09/12)^{25*12}-1}{0.09/12} \right ]$

$=1510.49\left [ \frac{8.40841}{0.0075} \right ]$

$=1693443$

Add down payment to this value, then you will get total cost of your house

i.e. $1,693,443 + $20,000 = $1,713,443

4.

To find remaining balance payment after 3 years:

$=PV(1+i/a)^{na}- A\left [ \frac{(1+i/a)^{na}}{i/a} \right ]$

Where, PV = Original balance

A = Installment/ payment

i = rate of interest

na = number of payments made till now.

number for payments made till the end of 3 years = 36

$=180,000(1+0.09/12)^{36}- 1510.49\left [ \frac{(1+0.09/12)^{36}}{0.09/12} \right ]$

$=173395.40$

Therefore, the remaining balance at the end of 3 years = $173,395.40

Payments made till 36th installment = 1510.49*36 = $54,377.64

Principal payment made = $180,000 - $173,395.40 = $6,604.60

Percentage of principal made in 36 payments = ($6,604.60 / $54,377.64)*100

= 12.15%

Note that i have rounded off the amounts to 2 decimals.