Use

PMT equals StartStartFraction Upper P left parenthesis StartFraction r Over n EndFraction right parenthesis OverOver 1 minus left parenthesis 1 plus StartFraction r Over n EndFraction right parenthesis Superscript negative nt EndEndFraction
 
to determine the regular payment​ amount, rounded to the nearest dollar. Your credit card has a balance of

​$4800
 
and an annual interest rate of

18

​%. 

With no further purchases charged to the card and the balance being paid off over

three
 
​years, the monthly payment is

​$174

​, 

and the total interest paid is

​$1464

. 

You can get a bank loan at

10.5

​% 

with a term of

four
 
years. Complete parts ​(a) and ​(b) below.

Question content area bottom

Part 1

a. How much will you pay each​ month? How does this compare with the​ credit-card payment each​ month? Select the correct choice below and fill in the answer boxes to complete your choice.

​(Do not round until the final answer. Then round to the nearest dollar as​ needed.)

A.

The monthly payments for the bank loan are approximately

​$enter your response here

. 

This is

​$enter your response here
 
more than the monthly​ credit-card payments.

B.

The monthly payments for the bank loan are approximately

​$enter your response here

. 

This is

​$enter your response here
 
less than the monthly​ credit-card payments.

To determine the monthly payment for the bank loan, we will use the PMT formula:

\[
\text{PMT} = \frac{P \left( \frac{r}{n} \right)}{1 - \left( 1 + \frac{r}{n} \right)^{-nt}}
\]

Where:
- $P$ is the loan amount (in this case, $4800).
- $r$ is the annual interest rate (10.5% = 0.105).
- $n$ is the number of payments per year (monthly payments, so $n = 12$).
- $t$ is the loan term in years (4 years).

Let's calculate the monthly payment (PMT):

1. $P = 4800$
2. $r = 0.105$
3. $n = 12$
4. $t = 4$

Substituting into the formula:

\[
\text{PMT} = \frac{4800 \left( \frac{0.105}{12} \right)}{1 - \left( 1 + \frac{0.105}{12} \right)^{-12 \times 4}}
\]

Let's calculate the monthly payment step by step.The monthly payment for the bank loan is approximately **$123**.

Now, let's compare this with the monthly credit card payment of **$174**.

Since $123 is less than $174, we'll calculate the difference:

\[
174 - 123 = 51
\]

So, the bank loan payment is **$51 less** than the monthly credit card payment.

Therefore, the correct option is:

**B**. The monthly payments for the bank loan are approximately **$123**. This is **$51 less** than the monthly credit card payments.

Would you like further details or have any questions?

Here are 5 related questions to expand on this:

1. How does the total interest paid over the bank loan term compare to the credit card interest?
2. What is the total amount paid over the 4-year loan term?
3. What would happen to the monthly payments if the loan term was reduced to 3 years?
4. How much would the monthly payment change if the interest rate were 12% instead of 10.5%?
5. Can making additional payments to the loan reduce the total interest paid?

**Tip:** A longer loan term generally results in lower monthly payments but higher total interest paid over time.

Use the PMT formula to determine the regular payment amount. Your credit card has a balance of $4800 and an annual interest rate of 18%. With no further purchases and the balance being paid off over 3 years, the monthly payment is $174, and the total interest paid is $1464. You can get a bank loan at 10.5% with a term of 4 years. Complete parts (a) and (b). Part 1 (a) asks for the monthly payments for the bank loan and a comparison with the credit card payments.

Learn how to calculate monthly loan payments using the PMT formula. This example involves a $4800 loan with a 10.5% interest rate over 4 years. Compare it to a credit card with an 18% interest rate paid off over 3 years. Ideal for students in Grades 10-12.

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