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• 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.

You want to buy a \$222,000 home.

A2 初級

# 比較兩種不同利率下的按揭付款（TI-84 TVM求解器）。 (Compare Mortgage Payments at Two Different Interest Rates (TI-84 TVM Solver))

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林宜悉 發佈於 2021 年 01 月 14 日