Pay serious attention to this section. This is the one that will most likely be useful in real life. Def: An annuity is a sequence of payments made at regular time intervals. Def: A sinking fund is an account set up for a specific purpose at a future date. For instance, retirement plans, setting up an account to save for a trip, or a way for a company to gain capital for a big purchase. Example 1: a) Suppose Fred wants to take a trip to Europe at the end of his college career. If Fred needs $4,500 for this trip, how much would he need to deposit into an account paying 8% year compounded quarterly if he expects to graduate 4 years from now? How much interest did he earn? b) George, Fred s twin brother, wants to also take this trip. However, he doesn t have the same account as Fred. Instead he will put a down payment of $100, and make monthly payments into an account with 8.25% interest compounded monthly. How much should each payment be? c) George decides to make $80 payments into the account. How much money would he have? Example 2: A corporation creates a sinking fund in order to have $810,000 to replace machinery in 10 years. The account is at 3.4% compounded weekly. a) How much should be placed into the account at the end of each week to meet this goal? b) How much is the account worth after 6 years?
Example 3: Suppose Diane is setting up for her retirement at 65. Until the age of 90, she wants her retirement to pay her $2000 a month. Starting at age 30, she wants to put her money in a monthly compounded account with an annual interest rate of 15%. a) How much should Diane have saved up at age 65? b) If Diane starts making monthly payments into the account when she is 30, how much should she deposit each month in order to reach this goal? Example 4: Andrea wishes to have her retirement account pay her $10,000 every quarter for 20 years after retirement. The account after retirement is at 4% per year compounded quarterly. In order to save this money, she makes a monthly deposit into an account paying interest at a rate of 5.5% per year compounded monthly. How much should she deposit each month in order to retire 35 years from now?
Def: The equity of a home (or any other piece of property) is the original value of the house what you still owe. It s a measure of how much of the property you own. When you get a loan, usually the bank wants some collateral: something that the bank can take if you don t pay your loan. Usually it s a house or some other property. In order to assess how much they can take from you, they ll want the equity of the property: how much that property is worth in your name. Example 5: A family gets a loan for a house for $250,000. The loan is at 8.2% yearly compounded every 2 months. The loan is to be paid off over 30 years. a) How much does the family pay every two months? b) How much does the family still owe after 12 years? c) What is the equity of the house after 12 years?
Example 6: A group of private investors purchased a condominium complex for $4 million. They made an initial down payment for 12% of the total and obtained a loan for the rest. The loan is to be paid off over 14 years at an interest rate of 11% per year compounded quarterly. a) What is the equity of the complex at the start of the loan? b) What is the quarterly payment for the loan? c) What is the equity of the complex after 10 years?
Amortization means paying off debt. It comes from the Latin word To Kill. We are killing our debt. Usually this is in the context of an amortization table. This table lists the payment made each period, how much goes to interest, how much goes towards the original balance of the loan, and how much of the original balance of the loan is left. When you make a payment, at the start, most goes towards interest, and a little towards the oustanding balance. As the loan progresses, you make the same payments, but less interest will be accruing on your balance, so more goes towards the principal. Example 7: Suppose I want a $5000 loan to build a Death Star. I got a loan, 10% compounded annually for 4 years. Fill in the amortization table for the loan. Example 8: Johnny wants to buy a $50,000 pirate ship in the Carribean. He puts $10,000 down and gets a loan for the rest. The loan is to be amortized over the next 10 years at a rate of 12% per year compounded monthly. a) Fill in the first 3 lines of the amortization table below: b) What is the equity of the ship after 6 years?