Math / Algebra

QuestionWhen Mary bought her condominium, she got her mortgage through a bank. The mortgage was a personal, amortized loan for $\$ 98,000$ , at an interest rate of $3.3 \%$ , with monthly payments for a term of 25 years. For each part, do not round any intermediate computations and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) Find Mary's monthly payment. $\$ 481.00$ (b) If Mary pays the monthly payment each month for the full term, find her total amount to repay the loan. $\$ 144,300$ (c) If Mary pays the monthly payment each month for the full term, find the total amount of interest she will pay. $\$ 46,300$

Studdy Solution

STEP 1

What is this asking? We need to figure out Mary's monthly mortgage payment, the total amount she'll repay, and how much of that is interest. Watch out! Don't mix up the loan amount with the total repayment, and remember interest is a big part of the cost!

STEP 2

1. Calculate Monthly Payment
2. Calculate Total Repayment
3. Calculate Total Interest Paid

STEP 3

Alright, so Mary's got this mortgage, right?
It's like a big promise to pay back the bank.
We've got the loan amount, which is $\$98,000$ , the interest rate, which is $3.3\%$ , and the loan term, which is $25$ years.
Let's break it down!

STEP 4

First, we need to convert the annual interest rate to a monthly rate.
We do this by dividing the annual rate by $12$ .
So, $3.3\%$ becomes $3.3\% / 12 = 0.033 / 12 = 0.00275$ .
This is our monthly interest rate.

STEP 5

Next, we need the number of total monthly payments.
Since the loan term is $25$ years, and there are $12$ months in a year, Mary will make $25 \cdot 12 = 300$ monthly payments.
This is our number of payments.

STEP 6

Now, we can use the monthly mortgage payment formula: $M = P \cdot \frac{r(1+r)^n}{(1+r)^n - 1}$ Where: $M$ is the monthly payment. $P$ is the principal loan amount ( $\$98,000$ ). $r$ is the monthly interest rate ( $0.00275$ ). $n$ is the total number of payments ( $300$ ).

STEP 7

Let's plug in the values: $M = \$98,000 \cdot \frac{0.00275(1+0.00275)^{300}}{(1+0.00275)^{300} - 1}$ $M = \$98,000 \cdot \frac{0.00275(1.00275)^{300}}{(1.00275)^{300} - 1}$ $M = \$98,000 \cdot \frac{0.00275 \cdot 2.2614}{2.2614 - 1}$ $M = \$98,000 \cdot \frac{0.00621885}{1.2614}$ $M = \$98,000 \cdot 0.0049306$ $M \approx \$483.20$

STEP 8

To find the total amount Mary repays, we multiply her monthly payment by the number of payments.

STEP 9

So, Total Repayment $= \$483.20 \cdot 300 = \$144,960$ .

STEP 10

The total interest paid is the difference between the total repayment and the original loan amount.

STEP 11

Therefore, Total Interest $= \$144,960 - \$98,000 = \$46,960$ .

STEP 12

(a) Mary's monthly payment is $\$483.20$ . (b) Mary's total repayment will be $\$144,960$ . (c) Mary will pay a total of $\$46,960$ in interest.

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Studdy Solution

STEP 1

What is this asking? We need to figure out Mary's monthly mortgage payment, the total amount she'll repay, and how much of that is interest. Watch out! Don't mix up the loan amount with the total repayment, and remember interest is a big part of the cost!

STEP 2

1. Calculate Monthly Payment
2. Calculate Total Repayment
3. Calculate Total Interest Paid

STEP 3

Alright, so Mary's got this mortgage, right?
It's like a big promise to pay back the bank.
We've got the loan amount, which is $\$98,000$ , the interest rate, which is $3.3\%$ , and the loan term, which is $25$ years.
Let's break it down!

STEP 4

First, we need to convert the annual interest rate to a monthly rate.
We do this by dividing the annual rate by $12$ .
So, $3.3\%$ becomes $3.3\% / 12 = 0.033 / 12 = 0.00275$ .
This is our monthly interest rate.

STEP 5

Next, we need the number of total monthly payments.
Since the loan term is $25$ years, and there are $12$ months in a year, Mary will make $25 \cdot 12 = 300$ monthly payments.
This is our number of payments.

STEP 6

Now, we can use the monthly mortgage payment formula: $M = P \cdot \frac{r(1+r)^n}{(1+r)^n - 1}$ Where: $M$ is the monthly payment. $P$ is the principal loan amount ( $\$98,000$ ). $r$ is the monthly interest rate ( $0.00275$ ). $n$ is the total number of payments ( $300$ ).

STEP 7

STEP 8

To find the total amount Mary repays, we multiply her monthly payment by the number of payments.

STEP 9

So, Total Repayment $= \$483.20 \cdot 300 = \$144,960$ .

STEP 10

The total interest paid is the difference between the total repayment and the original loan amount.

STEP 11

Therefore, Total Interest $= \$144,960 - \$98,000 = \$46,960$ .

STEP 12

(a) Mary's monthly payment is $\$483.20$ . (b) Mary's total repayment will be $\$144,960$ . (c) Mary will pay a total of $\$46,960$ in interest.

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Studdy Solution

STEP 1

What is this asking? We need to figure out Mary's monthly mortgage payment, the total amount she'll repay, and how much of that is interest. Watch out! Don't mix up the loan amount with the total repayment, and remember interest is a big part of the cost!

STEP 2

1. Calculate Monthly Payment2. Calculate Total Repayment3. Calculate Total Interest Paid

STEP 3

Alright, so Mary's got this mortgage, right?It's like a big promise to pay back the bank.We've got the **loan amount**, which is $98,000\$98,000$98,000, the **interest rate**, which is 3.3%3.3\%3.3%, and the **loan term**, which is 252525 years.Let's **break it down**!

STEP 4

First, we need to convert the annual interest rate to a monthly rate.We do this by dividing the annual rate by 121212.So, 3.3%3.3\%3.3% becomes 3.3%/12=0.033/12=0.002753.3\% / 12 = 0.033 / 12 = 0.002753.3%/12=0.033/12=0.00275.This is our **monthly interest rate**.

STEP 5

Next, we need the number of total monthly payments.Since the loan term is 252525 years, and there are 121212 months in a year, Mary will make 25⋅12=30025 \cdot 12 = 30025⋅12=300 monthly payments.This is our **number of payments**.

STEP 6

STEP 7

STEP 8

To find the total amount Mary repays, we multiply her **monthly payment** by the **number of payments**.

STEP 9

So, **Total Repayment** =$483.20⋅300=$144,960= \$483.20 \cdot 300 = \$144,960=$483.20⋅300=$144,960.

STEP 10

The total interest paid is the difference between the **total repayment** and the **original loan amount**.

STEP 11

Therefore, **Total Interest** =$144,960−$98,000=$46,960= \$144,960 - \$98,000 = \$46,960=$144,960−$98,000=$46,960.

STEP 12

(a) Mary's monthly payment is $483.20\$483.20$483.20. (b) Mary's total repayment will be $144,960\$144,960$144,960. (c) Mary will pay a total of $46,960\$46,960$46,960 in interest.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Calculate Monthly Payment
2. Calculate Total Repayment
3. Calculate Total Interest Paid

Alright, so Mary's got this mortgage, right?
It's like a big promise to pay back the bank.
We've got the loan amount, which is $\$98,000$ , the interest rate, which is $3.3\%$ , and the loan term, which is $25$ years.
Let's break it down!

First, we need to convert the annual interest rate to a monthly rate.
We do this by dividing the annual rate by $12$ .
So, $3.3\%$ becomes $3.3\% / 12 = 0.033 / 12 = 0.00275$ .
This is our monthly interest rate.

Next, we need the number of total monthly payments.
Since the loan term is $25$ years, and there are $12$ months in a year, Mary will make $25 \cdot 12 = 300$ monthly payments.
This is our number of payments.

To find the total amount Mary repays, we multiply her monthly payment by the number of payments.

So, Total Repayment $= \$483.20 \cdot 300 = \$144,960$ .

The total interest paid is the difference between the total repayment and the original loan amount.

Therefore, Total Interest $= \$144,960 - \$98,000 = \$46,960$ .

(a) Mary's monthly payment is $\$483.20$ . (b) Mary's total repayment will be $\$144,960$ . (c) Mary will pay a total of $\$46,960$ in interest.