You want to buy a $222,000 home.
You plan to pay 10% as a down payment and take
out a 30-year loan for the rest.
Part a, how much is the loan amount going to be?
Because you are putting 10% down, the loan amount
is going to be 90% of $222,000 since 100% minus 10% is 90%.
So for part a we have to find 90% of 222,000.
To find the percent of a number, we convert
the percent to a decimal and multiply.
90% as a decimal is 0.90, or just 0.9,
giving us 0.9 times 222,000.
And now going to the calculator
0.9 times 222,000 is 199,800 and therefore
the loan amount is $199,800.
And then for part b, what will your monthly
payments be if the interest is 6%?
To answer this question we will use the TI-84 TVM solver.
Let's begin by determining the required
information below where capital N is the total
number of payment periods.
Because you are paying monthly for a period
of 30 years, capital N is 30 times 12, which is 360.
There are 360 months in 30 years.
I% for part b is 6% and therefore we enter six here.
PV stands of present value, which is a beginning
loan amount, which we now know is 199,800.
This is positive because you are receiving
that amount of money.
PMT stands for payment amount, which we are solving for.
FV stands for future value, which is zero
because after 30 years the loan is paid off
and the balance is zero.
And payments per year and compounds per year
will both be 12 because you are paying monthly
and we assume the interest is compounded monthly.
And we always leave the PMT option at the bottom set on end.
And now we go to the calculator
and then we press apps, enter, enter,
then enter the information.
Capital N is 360, enter.
I% is six, enter.
PV is 199,800, this is the present value, enter.
We are solving for the payment, so we'll come
back to this row, enter.
Future value is zero, enter.
And payments per year and compounds per year are both 12.
And notice how we do have PMT set on end.
To solve for the monthly payment we go up
to the row for PMT or payment and press alpha, enter.
Notice how it's negative because this
is the amount you have to pay each month
which means the monthly payment when the interest
rate is 6% is $1,197.90 to the nearest cent.
So using the solver, even though the PMT
amount is negative, we do enter a positive value
for part b for the monthly payments.
And then for part c, what will your monthly
payments be if the interest rate is 7%?
To answer this question using the TVM solver
we simply change the 6% to 7% and then solve for PMT again.
So going back to the calculator, again we change
the six to a seven for the interest rate.
Everything else stays the same.
And now we go down and solve for the payment again.
So go down to the payment row, the cursor does
have to be in this row to solve for this,
and then we press alpha, enter.
So if the interest rate changes to 7%
then the monthly payments are going to be $1,329.27.
Looking at the monthly payments, notice how
when the interest rate goes up from 6% to 7%
the monthly payment goes up by over $130
which is why the interest rate of a mortgage
is so important.
I hope you found this helpful.