A loan used for buying a home is called a mortgage. The...

A loan used for buying a home is called a mortgage. The Fortunato family is buying a $\$ 430,000$ home. They are taking out a 30 -year mortgage at a rate of 8$\% .$ a. Compute the monthly payment. b. Find the total of all of the monthly payments for the 30 years. c. What is the fi nance charge? d. Which is greater, the interest or the original cost of the home?

A loan used for buying a home is called a mortgage. The Fortunato family is buying a $\$ 430,000$ home. They are taking out a 30 -year mortgage at a rate of 8$\% .$
a. Compute the monthly payment.
b. Find the total of all of the monthly payments for the 30 years.
c. What is the fi nance charge?
d. Which is greater, the interest or the original cost of the home?

Key Concepts

Mortgage

A mortgage is a type of loan used to purchase real estate where the property itself serves as collateral. It involves borrowing a principal amount and repaying it over time with added interest, securely tied to the property until the debt is fully repaid.

Interest Rate

The interest rate is the percentage at which interest accrues on the borrowed principal over time. It determines the cost of borrowing and directly impacts the amount of each payment that goes toward interest versus reducing the principal.

Amortization

Amortization is the process of spreading out a loan into a series of fixed payments over time. Each payment includes both principal and interest, and as the principal decreases, the interest portion of each subsequent payment typically diminishes.

Monthly Payment Calculation

Calculating the monthly payment for a mortgage uses an annuity formula that takes into account the principal, the periodic interest rate, and the total number of payments over the loan term. This fixed monthly payment ensures that the loan is fully paid off by the end of the term.

Finance Charge

The finance charge is the total cost of borrowing, representing the aggregate amount of interest paid over the life of the loan. It highlights the extra amount paid beyond the original principal due to the interest rate applied over time.

Loan Term

The loan term is the duration over which the debt is scheduled to be repaid. The length of the loan term affects the size of the monthly payments and the overall interest paid during the life of the mortgage.

Transcript

00:01 Family bought a $430 ,000 home at 8 % interest over a 30 -year mortgage.

00:06 We want to find out the monthly payments.

00:08 And another way to say that is the emi, the equated monthly installments.

00:12 This works for cars.

00:15 I mean, pretty much anything where you're paying monthly installments.

00:19 And so p is going to be the principal.

00:22 So let's go ahead and put $430 ,000 there.

00:26 The equation looks a lot more intimidating than it turns out to be.

00:30 So if you're looking at that and you're like, oh, my, just hang in there.

00:35 The r is the interest rate, which is 0 .08.

00:40 And pretty soon this problem is going to turn into why 8 % finance rate apr financing is not a good idea.

00:48 1 plus 0 .08.

00:51 By the way, the 12s that are in this equation are because of the monthly payments.

00:57 And so n is 12 in that case.

00:59 And then t, of course, is the time in gear, so we're going to do 30 for that, 30 -year mortgage.

01:10 Okay, all of that divided by 1 plus 0 .08 divided by 12, all to the power of 12 times t, which is 30, and then minus 1.

01:34 Now, if you put this in the calculator, just make sure that you bracket the whole denominator with parentheses down there.

01:41 And i'm just doing one quick double check here, just to make sure we're all good.

01:46 And yes, that should be good there.

01:49 And so that is going to end up becoming.

01:51 I'll go ahead and write it over to the right.

01:53 The monthly installments are going to be 3 ,155 .187, or we could just round it to 19 cents.

02:07 So that is the answer to part a there.

02:10 And then for part b, they're wondering what the total amount is going to be that you're going to have to pay.

02:18 And so we're going to multiply that amount that we just got an a times 12 to get for a full year since it's per month there...

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