Professor Shoemaker When you borrow money you must eventually return the amount you borrow And you also pay an additional amount which is rent on the use of the money while you have it and the lender doesn t Excel 2 Excel 1
Borrowing money is like renting an apartment When you rent an apartment, you have to give it back when you re done. And you rent for your use of the apartment while you have it Excel 3 The money you pay back is in two parts Principle - the amount you borrowed Interest - the rent you pay to use the money Excel 4 Excel 2
If you borrow $10,000 at 5% interest and agree to pay it all back with interest in one payment at the end of the year You ll return the $10,000 principle And you ll pay an additional $500 in interest ($10,000 * 5% = $500) For a total of $10,500 Excel 5 The value of money is determined in part by affect of time Money and time affect each other You can t figure one without understanding the other It s crucial in understanding loan concepts to keep track of both money and time Excel 6 Excel 3
Suppose you paint houses over the summer. You give two people estimates for $4,000. Both accept your offer, but one person says he will pay you when the work is done and the other says he ll pay you at the end of the year when he gets his year-end bonus. Excel 7 Payment at the end of the job or the end of year Which deal is more valuable to you? Why? What s really going on with the second deal? Excel 8 Excel 4
Present Value The value of an amount of money right now What is the Present Value of the $4,000 when you re paid immediately at the end of the job? What is the Present Value of the $4,000 when you have to wait to the end of the year to be paid? Excel 9 Future Value The value of an amount of money at some point in the future The Future Value of an amount of money is normally lower its Present Value. Why? Excel 10 Excel 5
Period The how often loan payments occur Typically monthly, quarterly or annually Watch out! In loan calculations we use the period and while it s often a month but it might be different Excel 11 Number of periods The number of periods in the life of a loan A five year car loan with monthly payments has 60 periods A 10 year CD with quarterly payments has 40 periods Watch out! It s the life of the loan, not the number of periods in a year. Excel 12 Excel 6
Payment The amount of the payment made each period In this class we ll assume all payments in a loan are the same, except for a possible balloon payment. Excel 13 When you borrow money to buy a car you are borrower and the bank is the lender When you put money into a savings account the bank is the borrower and you are the lender Excel 14 Excel 7
Two Concepts that trip up many students 1. The direction of the flow of money determines the sign (+/-) of the amount 2. The loan s payment period may not be a monthly Excel 15 It s very important in working with loans to keep track of the direction that money is flowing Is it flowing toward you or away from you? The sign for money flowing toward you is positive Money you borrow flows toward you and is a positive number The sign for money flowing away from you is negative. When you make a payment on a loan the money is flowing away from you and so is a negative number Excel 16 Excel 8
The Number of Periods is the number of payments in the life of a loan, not in a year If the period is monthly, there are 12 periods in a year So, there are 60 payments in a 5 year loan Excel 17 13-Loans.xlsx Excel 18 Excel 9
Present Value of the Loan is the amount you re borrowing This loan has monthly payments Excel 19 Note how the Rate and Nper arguments are setup. Why are they this way? What is the sign of the result of the PMT function? Why? Excel 20 Excel 10
RATE NPER PV The Rate per period The Number of Periods in the life of the loan The Present Value of the loan. AKA the principle. Excel 21 When you are the borrower The amount you borrow from the bank (PV) will be positive since it s money flowing TOWARD you. The Payment amount (PMT) will be negative since it s money flowing AWAY from you. Excel 22 Excel 11
The loan amount (PV) is always positive Your payment (PMT) is always negative Excel 23 Lenders often charge various fees to make a loan Points Each point is 1% of the value of the loan Application fees The charge for applying for a mortgage. The effect of fees and points is to increase your cost of borrowing In a sense, you re borrowing the money for the points and fees The APR takes those costs into consideration Excel 24 Excel 12
In this example, the fee and points add up to $2,100 ($300 + $1,800) While the loan is for $90,000 you re receiving only $87,900 from the bank Excel 25 The payment of $456.02 is based on $90,000, but you re receiving only $87,900. Thus the rate you re paying is really higher than 4.5%. It s actually 4.7%. Excel 26 Excel 13
No matter the number of years in a mortgage, you re really borrowing money month by month. The payment stays the same every month The amount going to pay off the principle and the amount paid in interest that month changes. Excel 27 As time goes by the amount of each payment going to interest declines and the amount going to the principle increases. Excel 28 Excel 14
The value of money is determined in part by effect of time Watch out for The direction of the flow of money determines the sign (+/-) of the amount The period of a loan many not be a year Excel 29 Excel 15