Math / Algebra

QuestionJoe and Sarah have been making regular monthly payments of $\$1264.14$ on their 30-year, $\$200{,}000$ mortgage at $6.5\%$ annual interest. After 11 payments, their principal is $\$197{,}956.38$ . To the nearest cent, how much of their next payment will go to pay interest?
A. $\$1327.34$ B. $\$1237.95$ C. $\$1251.01$ D. $\$1072.26$

Studdy Solution

STEP 1

What is this asking? How much of Joe and Sarah's next mortgage payment goes towards interest, given their current principal, interest rate, and payment amount? Watch out! Don't forget to convert the annual interest rate to a monthly rate!

STEP 2

1. Calculate the monthly interest rate.
2. Calculate the interest portion of the next payment.

STEP 3

Alright, so we're given an annual interest rate of $6.5\%$ , but we need the monthly rate since they're making monthly payments.
To get the monthly rate, we divide the annual rate by 12!

STEP 4

$6.5\% = \frac{6.5}{100} = 0.065$ So, $6.5\%$ is the same as $0.065$ .

STEP 5

Now, let's divide this by $\bf{12}$ to get our monthly rate: $\frac{0.065}{12} \approx 0.00541667$ This means the monthly interest rate is approximately $0.00541667$ .

STEP 6

We know their current principal is $\$\bf{197{,}956.38}$ and the monthly interest rate is approximately $0.00541667$ .
To find the interest portion of their next payment, we simply multiply these two values!

STEP 7

$\$\bf{197{,}956.38} \cdot 0.00541667 \approx \$\bf{1072.26}$ So, the interest portion of their next payment will be approximately $\$\bf{1072.26}$ !

STEP 8

The interest portion of Joe and Sarah's next mortgage payment will be approximately $\$1072.26$ , which corresponds to answer choice D.

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Studdy Solution

STEP 1

What is this asking? How much of Joe and Sarah's next mortgage payment goes towards interest, given their current principal, interest rate, and payment amount? Watch out! Don't forget to convert the annual interest rate to a monthly rate!

STEP 2

1. Calculate the monthly interest rate.
2. Calculate the interest portion of the next payment.

STEP 3

Alright, so we're given an annual interest rate of $6.5\%$ , but we need the monthly rate since they're making monthly payments.
To get the monthly rate, we divide the annual rate by 12!

STEP 4

$6.5\% = \frac{6.5}{100} = 0.065$ So, $6.5\%$ is the same as $0.065$ .

STEP 5

Now, let's divide this by $\bf{12}$ to get our monthly rate: $\frac{0.065}{12} \approx 0.00541667$ This means the monthly interest rate is approximately $0.00541667$ .

STEP 6

We know their current principal is $\$\bf{197{,}956.38}$ and the monthly interest rate is approximately $0.00541667$ .
To find the interest portion of their next payment, we simply multiply these two values!

STEP 7

$\$\bf{197{,}956.38} \cdot 0.00541667 \approx \$\bf{1072.26}$ So, the interest portion of their next payment will be approximately $\$\bf{1072.26}$ !

STEP 8

The interest portion of Joe and Sarah's next mortgage payment will be approximately $\$1072.26$ , which corresponds to answer choice D.

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Studdy Solution

STEP 1

What is this asking? How much of Joe and Sarah's next mortgage payment goes towards interest, given their current principal, interest rate, and payment amount? Watch out! Don't forget to convert the annual interest rate to a monthly rate!

STEP 2

1. Calculate the monthly interest rate.2. Calculate the interest portion of the next payment.

STEP 3

Alright, so we're given an **annual interest rate** of 6.5%6.5\%6.5%, but we need the *monthly* rate since they're making monthly payments.To get the monthly rate, we **divide** the annual rate by **12**!

STEP 4

6.5%=6.5100=0.0656.5\% = \frac{6.5}{100} = 0.0656.5%=1006.5​=0.065 So, 6.5%6.5\%6.5% is the same as 0.0650.0650.065.

STEP 5

Now, let's **divide** this by 12\bf{12}12 to get our monthly rate: 0.06512≈0.00541667\frac{0.065}{12} \approx 0.00541667120.065​≈0.00541667 This means the **monthly interest rate** is approximately 0.005416670.005416670.00541667.

STEP 6

We know their current principal is $197,956.38\$\bf{197{,}956.38}$197,956.38 and the **monthly interest rate** is approximately 0.005416670.005416670.00541667.To find the interest portion of their next payment, we simply **multiply** these two values!

STEP 7

$197,956.38⋅0.00541667≈$1072.26\$\bf{197{,}956.38} \cdot 0.00541667 \approx \$\bf{1072.26}$197,956.38⋅0.00541667≈$1072.26 So, the interest portion of their next payment will be approximately $1072.26\$\bf{1072.26}$1072.26!

STEP 8

The interest portion of Joe and Sarah's next mortgage payment will be approximately $1072.26\$1072.26$1072.26, which corresponds to answer choice D.

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1. Calculate the monthly interest rate.
2. Calculate the interest portion of the next payment.

Alright, so we're given an annual interest rate of $6.5\%$ , but we need the monthly rate since they're making monthly payments.
To get the monthly rate, we divide the annual rate by 12!

$6.5\% = \frac{6.5}{100} = 0.065$ So, $6.5\%$ is the same as $0.065$ .

Now, let's divide this by $\bf{12}$ to get our monthly rate: $\frac{0.065}{12} \approx 0.00541667$ This means the monthly interest rate is approximately $0.00541667$ .

We know their current principal is $\$\bf{197{,}956.38}$ and the monthly interest rate is approximately $0.00541667$ .
To find the interest portion of their next payment, we simply multiply these two values!

$\$\bf{197{,}956.38} \cdot 0.00541667 \approx \$\bf{1072.26}$ So, the interest portion of their next payment will be approximately $\$\bf{1072.26}$ !

The interest portion of Joe and Sarah's next mortgage payment will be approximately $\$1072.26$ , which corresponds to answer choice D.