Chapter 8 Mortgages
Lecture 18: Mortgages
Learning Outcomes:
- Define amortization and explain its purpose in loan repayment.
- Identify the components of an amortization schedule: payment number, payment amount, interest portion, principal portion, and remaining balance.
- Calculate the periodic payment (PMT) for a fully amortized loan using the appropriate time value of money formulas.
- Construct a complete amortization table for a fixed-rate loan using given loan terms.
- Distinguish between interest and principal components in each payment.
Review Problems From Last Lecture:
- A retiree plans to purchase a deferred annuity that will pay $2,000 per month, with the first payment exactly 10 years from now, and will continue for 20 years. The annuity earns an interest rate of 6% compounded monthly. What is the present value of the annuity (i.e., how much should the retiree invest today to receive this income stream)?
- An investor wants to purchase a deferred perpetuity that will pay $5,000 annually, starting 8 years from today and continuing forever. The annual interest rate is 7%, compounded annually. What is the present value of this investment today?
- Maria decides to invest in her RRSP to prepare for retirement. She contributes $6,000 at the end of each year for 20 years. The account earns an annual interest rate of 5%, compounded annually. After the 20 years of contributions, Maria stops adding money to the RRSP and allows the investment to grow with compound interest for another 10 years without any withdrawals. At the end of this 10-year accumulation period, Maria begins withdrawing $25,000 at the end of each year for her retirement. The account continues to earn 5% interest, compounded annually, during the withdrawal phase.
- What will be the value of Maria’s RRSP at the time she stops contributing (i.e., after 20 years)?
- What will be the value of the RRSP at the beginning of the withdrawal phase (i.e., after the additional 10 years of interest accumulation)?
- For how many years will Maria be able to withdraw $25,000 annually before the RRSP is depleted?
Lecture Notes:
Lecture material for this class come from Sections 8.1 and can be found below. This material is considered review material and so it is not covered in depth.
- Video: Loan Amortization Schedules
Video: Mortgages
An amortization table shows how a loan is repaid over time through regular periodic payments. Each payment consists of both interest and principal components.
Purpose- To track how much of each payment goes toward interest vs. principal.
- To monitor the remaining loan balance after each payment.
- To understand the cost of borrowing over time.
Key Components of an Amortization Table
- Payment Number (e.g., 1, 2, 3, …, \(n\))
- Payment Amount (fixed for a level-payment loan)
- Interest Portion = Current balance \(\times\) periodic interest rate
- Principal Portion = Total payment \(-\) interest
- Remaining Balance = Previous balance \(-\) principal paid
Important Notes
- The interest portion decreases over time.
- The principal portion increases over time.
- The loan is fully paid off at the end of the amortization period.
- Total interest paid can be significant, especially for long-term loans.
Lecture Problems:
- You borrow $10,000 and will repay it with $3000 payments at the end of each year. Create a loan repayment schedule. Use 5% annually compounded interest.
- ou need $450,000 for your mortgage. You repay this back over some period of time with biweekly payments of $1,400. Create a loan repayment schedule detailing the first 3 lines and the last 2 lines of the repayment schedule. The mortgage rate is 4% compounded semi-annually.