Smith has arranged for a mortgage loan of $200,000. The annual rate on the loan is 12%. The bank requires Mr. Smith to make payments of $4,212.90 at the end of every month. How many payments will Mr. Smith have to make?
Smith has arranged for a mortgage loan of $200,000. The annual rate on the loan is 12%. The bank requires Mr. Smith to make payments of $4,212.90 at the end of every month. How many payments will Mr. Smith have to make?
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
Related questions
Question
100%
- Smith has arranged for a mortgage loan of $200,000. The annual rate on the loan is 12%. The bank requires Mr. Smith to make payments of $4,212.90 at the end of every month. How many payments will Mr. Smith have to make?
- You have decided to buy a car, the price of the car is $18,000. The car dealer presents you with two choices:
- Purchase the car for cash and receive $2000 instant cash rebate – your out of pocket expense is $16,000 today.
- Purchase the car for $18,000 with zero percent interest 36-month loan with monthly payments.
The market interest rate is 4%. Which of the option above is cheaper? How much do you save?
![### Future and Present Value
1. **Future Value (FV) of a Lump Sum**
\[
FV = C(1 + r)^T
\]
2. **Present Value (PV) of a Lump Sum**
\[
PV = \frac{D}{(1 + r)^T}
\]
3. **Future Value in terms of Present Value**
\[
FV = PV(1 + r)^T
\]
4. **Rate of Return (r) Calculation**
\[
r = \left(\frac{FV}{PV}\right)^{\frac{1}{T}} - 1
\]
5. **Time Period (T) Calculation**
\[
T = \frac{\ln\left(\frac{FV}{PV}\right)}{\ln(1 + r)}
\]
### Annuity
1. **Present Value (PV) of an Annuity**
\[
PV = \frac{pmt}{r} \left[1 - \frac{1}{(1 + r)^T}\right]
\]
2. **Payment (pmt) Calculation**
\[
pmt = \frac{PV \cdot r}{\left[1 - \frac{1}{(1 + r)^T}\right]}
\]
3. **Time Period (T) for Annuity**
\[
T = \frac{\ln(pmt) - \ln(pmt - PV \cdot r)}{\ln(1 + r)}
\]
4. **Future Value (FV) of an Annuity**
\[
FV = \frac{pmt}{r} \left[(1 + r)^T - 1\right]
\]
### Annuity Due
5. **Present Value (PV) of an Annuity Due**
\[
PV = \frac{pmt}{r} \left[1 - \frac{1}{(1 + r)^T}\right] (1 + r)
\]
6. **Future Value (FV) of an Annuity Due**
\[
FV = \frac{pmt}{r} \left[(1 + r)^T - 1\right](1 + r)
\]
### EAR & APR
1. **Effective Annual](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F10c7525c-c416-4320-97b0-471febd6b171%2F7e60fa80-9841-48a2-9588-75d0f7293843%2F9glf8b9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Future and Present Value
1. **Future Value (FV) of a Lump Sum**
\[
FV = C(1 + r)^T
\]
2. **Present Value (PV) of a Lump Sum**
\[
PV = \frac{D}{(1 + r)^T}
\]
3. **Future Value in terms of Present Value**
\[
FV = PV(1 + r)^T
\]
4. **Rate of Return (r) Calculation**
\[
r = \left(\frac{FV}{PV}\right)^{\frac{1}{T}} - 1
\]
5. **Time Period (T) Calculation**
\[
T = \frac{\ln\left(\frac{FV}{PV}\right)}{\ln(1 + r)}
\]
### Annuity
1. **Present Value (PV) of an Annuity**
\[
PV = \frac{pmt}{r} \left[1 - \frac{1}{(1 + r)^T}\right]
\]
2. **Payment (pmt) Calculation**
\[
pmt = \frac{PV \cdot r}{\left[1 - \frac{1}{(1 + r)^T}\right]}
\]
3. **Time Period (T) for Annuity**
\[
T = \frac{\ln(pmt) - \ln(pmt - PV \cdot r)}{\ln(1 + r)}
\]
4. **Future Value (FV) of an Annuity**
\[
FV = \frac{pmt}{r} \left[(1 + r)^T - 1\right]
\]
### Annuity Due
5. **Present Value (PV) of an Annuity Due**
\[
PV = \frac{pmt}{r} \left[1 - \frac{1}{(1 + r)^T}\right] (1 + r)
\]
6. **Future Value (FV) of an Annuity Due**
\[
FV = \frac{pmt}{r} \left[(1 + r)^T - 1\right](1 + r)
\]
### EAR & APR
1. **Effective Annual
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
Recommended textbooks for you
Essentials Of Investments
Finance
ISBN:
9781260013924
Author:
Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:
Mcgraw-hill Education,
Essentials Of Investments
Finance
ISBN:
9781260013924
Author:
Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:
Mcgraw-hill Education,
Foundations Of Finance
Finance
ISBN:
9780134897264
Author:
KEOWN, Arthur J., Martin, John D., PETTY, J. William
Publisher:
Pearson,
Fundamentals of Financial Management (MindTap Cou…
Finance
ISBN:
9781337395250
Author:
Eugene F. Brigham, Joel F. Houston
Publisher:
Cengage Learning
Corporate Finance (The Mcgraw-hill/Irwin Series i…
Finance
ISBN:
9780077861759
Author:
Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan Professor
Publisher:
McGraw-Hill Education