Determine the monthly payment for a $30000 car with no downpayment, using 12% annual financing for a period of 5 years. Pmt P r/(1 -1.r^-t) Be sure to adjust r to monthly and t to months. One.
Determine the monthly payment for a $30000 car with no downpayment, using 12% annual financing for a period of 5 years. Pmt P r/(1 -1.r^-t) Be sure to adjust r to monthly and t to months. One.
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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![### Financial Mathematics Problems
#### Problem One:
**Determine the monthly payment for a $30,000 car with no down payment, using 12% annual financing for a period of 5 years.**
To find the monthly payment (Pmt), you can use the formula:
\[ \text{Pmt} = \frac{P * r}{1 - (1 + r)^{-t}} \]
- **P** - Principal loan amount ($30,000)
- **r** - Monthly interest rate (annual rate of 12% divided by 12 months)
- **t** - Total number of payments (loan period in months, 5 years * 12 months/year)
**Steps:**
1. Convert annual rate to monthly rate:
\[
\text{Monthly rate} = \frac{12\%}{12} = 1\%
\\
r = \frac{12}{100 \times 12} = 0.01
\]
2. Convert loan period to months:
\[
t = 5 \text{ years} \times 12 \text{ months/year} = 60 \text{ months}
\]
3. Substitute these values into the formula:
\[
\text{Pmt} = \frac{30,000 \times 0.01}{1 - (1 + 0.01)^{-60}}
\]
#### Problem Two:
**Credit Card Cycle:**
- **Beginning balance:** $2000
- **Annual rate:** 24%, which translates to 2% monthly
- **Purchases this month:** $145
- **Minimum payment per month:** $100
**Determine the ending balance.**
**Steps:**
1. Calculate interest for the month:
\[
\text{Interest} = \text{Beginning balance} \times \text{Monthly rate}
\\
= 2000 \times 0.02 = 40
\]
2. Add purchases and interest to the beginning balance:
\[
\text{New balance before payment} = 2000 + 40 + 145 = 2185
\]
3. Subtract the minimum payment:
\[
\text{Ending balance} = 2185 - 100 = 2085
\]
Thus, the ending balance of the credit card for](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe81fc724-95ca-442b-b1f9-11ea5ce9f932%2F94af5ee6-d09c-412c-9151-d21b2d5512ae%2Fvscl9q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Financial Mathematics Problems
#### Problem One:
**Determine the monthly payment for a $30,000 car with no down payment, using 12% annual financing for a period of 5 years.**
To find the monthly payment (Pmt), you can use the formula:
\[ \text{Pmt} = \frac{P * r}{1 - (1 + r)^{-t}} \]
- **P** - Principal loan amount ($30,000)
- **r** - Monthly interest rate (annual rate of 12% divided by 12 months)
- **t** - Total number of payments (loan period in months, 5 years * 12 months/year)
**Steps:**
1. Convert annual rate to monthly rate:
\[
\text{Monthly rate} = \frac{12\%}{12} = 1\%
\\
r = \frac{12}{100 \times 12} = 0.01
\]
2. Convert loan period to months:
\[
t = 5 \text{ years} \times 12 \text{ months/year} = 60 \text{ months}
\]
3. Substitute these values into the formula:
\[
\text{Pmt} = \frac{30,000 \times 0.01}{1 - (1 + 0.01)^{-60}}
\]
#### Problem Two:
**Credit Card Cycle:**
- **Beginning balance:** $2000
- **Annual rate:** 24%, which translates to 2% monthly
- **Purchases this month:** $145
- **Minimum payment per month:** $100
**Determine the ending balance.**
**Steps:**
1. Calculate interest for the month:
\[
\text{Interest} = \text{Beginning balance} \times \text{Monthly rate}
\\
= 2000 \times 0.02 = 40
\]
2. Add purchases and interest to the beginning balance:
\[
\text{New balance before payment} = 2000 + 40 + 145 = 2185
\]
3. Subtract the minimum payment:
\[
\text{Ending balance} = 2185 - 100 = 2085
\]
Thus, the ending balance of the credit card for
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