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Learning Objectives – Class 1
After today’s lecture, and after working the homework problems, the student should be able to
- Explain why people borrow and loan money, and under what conditions.
- Compute total interest paid on a loan.
- Draw basic cash flow diagrams and generate cash flow tables for amounts of money expended and brought in on a project at various times during the life of a project.
- Determine the amount of money remaining due on a loan after some number of years, including compound interest.
- Show economic transactions in either table or cash flow diagram fashion.
Topics covered in today’s class
A typical loan for $100,000 at interest rate of 10% per year, compounded yearly, is shown below. Both the borrower and the lender think they are getting a good deal, and cannot find a better deal elsewhere. All aspects of the loan were negotiated and agreed to by both the lender and the borrower, including the amount borrowed, the length of the loan, the interest rate, and the repayment schedule. Other agreements could include penalty for early payment of loan, penalties for missing payments, etc. Several POSSIBLE loan repayment schedules are shown below – the first where no payments are made until the end of the loan, the second where all interest and only interest is repaid at the end of each compounding period (called an Interest Only Loan), and the third where payments are sporadic, but acceptable to the lender and manageable by the borrower. Note also that when a bank says 6% interest, they mean, by law, 6% nominal per year, not 6% per month, not 6% per day, not … If you borrow the money from the Mafia, they may have different rules (like 6% might mean 6% per day) but you will have to discuss that with them.
1) Why might the borrower want to enter into each of these agreements?
2) Why might the lender want to enter into each of these agreements?
3) What downsides might the lender face?
4) What downsides might the borrower face?
5) Note CAREFULLY the numbering scheme used for n, and recognize that if you are not faced with a “standard” case, you will HAVE to convert your problem to STANDARD FORM!
6) Note that a loan is comprised of two items, Principal and Interest. How do you calculate the interest? Total paid – Amount borrowed = interest paid.
7) Note standard names used: P = Present, F = Future, A = Annual, G = Gradient, etc.
8) 6%, by law, means 6% nominal interest per year.
9) Compounding periods can be yearly, monthly, daily, secondly, etc.
9a) For various ways of paying back a $100,000 loan at 10% nominal interest rate
What if we make no annual payments and pay off the loan at the end of 5 years?
| End of Year | Amount | Interest | Amount | Amount Owed During | ||
| Borrowed | Owed | Paid | Compounding Period | |||
| 0 | $100,000 | $0 | $0 | $100,000 | ||
| 1 | $10,000 | $0 | $110,000 | |||
| 2 | $11,000 | $0 | $121,000 | |||
| 3 | $12,100 | $0 | $133,100 | |||
| 4 | $13,310 | $0 | $146,410 | |||
| 5 | $14,641 | $161,051 | $0 | |||
| Total Paid to Lender = | $161,051 | |||||
| Total Interest Paid to Lender = | $61,051 | |||||
9b) What if we make interest only annual payments and pay off the loan at the end of 5 years?
| End of Year | Amount | Interest | Amount | Amount Owed During | ||
| Borrowed | Owed | Paid | Compounding Period | |||
| 0 | $100,000 | $0 | $0 | $100,000 | ||
| 1 | $10,000 | $10,000 | $100,000 | |||
| 2 | $10,000 | $10,000 | $100,000 | |||
| 3 | $10,000 | $10,000 | $100,000 | |||
| 4 | $10,000 | $10,000 | $100,000 | |||
| 5 | $10,000 | $110,000 | $0 | |||
| Total Paid to Lender = | $150,000 | |||||
| Total Interest Paid to Lender = | $50,000 | |||||
9c) What if we make strange annual payments and pay off the loan at the end of 5 years?
| End of Year | Amount | Interest | Amount | Amount Owed During | ||
| Borrowed | Owed | Paid | Compounding Period | |||
| 0 | $100,000 | $0 | $0 | $100,000 | ||
| 1 | $10,000 | $7,000 | $103,000 | |||
| 2 | $10,300 | $20,000 | $93,300 | |||
| 3 | $9,330 | $0 | $102,630 | |||
| 4 | $10,263 | $30,000 | $82,893 | |||
| 5 | $8,289 | $91,182 | $0 | |||
| Total Paid to Lender = | $148,182 | |||||
| Total Interest Paid to Lender = | $48,182 | |||||
9d) What if we to pay off the loan early?
| End of Year | Amount | Interest | Amount | Amount Owed During | ||
| Borrowed | Owed | Paid | Compounding Period | |||
| 0 | $100,000 | $0 | $0 | $100,000 | ||
| 1 | $10,000 | $7,000 | $103,000 | |||
| 2 | $10,300 | $20,000 | $93,300 | |||
| 3 | $9,330 | $0 | $102,630 | |||
| 4 | $10,263 | $112,893 | $0 | <-Different here | ||
| 5 | $0 | $0 | $0 | |||
| Total Paid to Lender = | $139,893 | |||||
| Total Interest Paid to Lender = | $39,893 | |||||
9e) What if we designate whether we wish our payments to go to principal or to interest?
| End of Year | Amount | Interest | Pay on | Pay on | Amount Owed During | |
| Borrowed | Owed | Principal | Interest | Compounding Period | ||
| 0 | $100,000 | $0 | $0 | $100,000 | ||
| 1 | $10,000 | $0 | $7,000.00 | $103,000 | ||
| 2 | $10,300 | $20,000 | $0.00 | $93,300 | ||
| 3 | $9,330 | $0 | $0.00 | $102,630 | ||
| 4 | $10,263 | $15,000 | $15,000.00 | $82,893 | ||
| 5 | $8,289 | $91,182 | $0.00 | $0 | ||
| Total Paid to Lender = | $148,182 | |||||
| Total Interest Paid to Lender = | $48,182 | |||||
9f) What if we designate whether we wish our payments to go to principal or interest?
| End of Year | Amount | Interest | Pay on | Pay on | Amount Owed During | |
| Borrowed | Owed | Principal | Interest | Compounding Period | ||
| 0 | $100,000 | $0 | $0 | $100,000 | ||
| 1 | $10,000 | $7,000 | $0.00 | $103,000 | ||
| 2 | $10,300 | $0 | $20,000.00 | $93,300 | ||
| 3 | $9,330 | $0 | $0.00 | $102,630 | ||
| 4 | $10,263 | $15,000 | $15,000.00 | $82,893 | ||
| 5 | $8,289 | $0 | $91,182.00 | $0 | ||
| Total Paid to Lender = | $148,182 | |||||
| Total Interest Paid to Lender = | $48,182 | |||||