Units 4A and 4B : Worksheet

Units 4A and 4B : Worksheet

Simple Interest Example: Suppose you invest $1000 for 3 years at an annual simple interest rate of 5.5%. How much money will be in your account at the end of 3 years?

Compounding the interest: Compound Interest is interest paid on interest reinvested with the principal, usually periodically. This can be done semi-annually, quarterly, monthly, daily, or continuously.

Example: Consider the first example. Keep the same initial deposit, same interest rate, And add compounding semi-annually. How much money is in the account at the end of 3 years?

A new formula: A = P(1 + i)n

APR = annual percentage rate. If the compounding is done annually, you can still use the above formula, you don't need a new one Similarly to what we did yesterday, Relative increase = AbsoluteIncrease

Starting Pr incipal For a 1 year period, the relative increase is called the APY, annual percentage yield.

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Example: How much should you invest now at 10% compounded quarterly to have$18,000 toward the purchase of a car in 5 years?

Continuous Compounding of Interest:

Exercise: Complete the following table for the given expression:

n

10 100 1000 10,000 100,000 1,000,000 10,000,000 100,000,000

1 + 1 n n

A new formula: A = Pert Used for compounding continuously.

Example: Compare $10,000 compounded quarterly for 15 years with the same amount compounded continuously for 5 years.

-34B. Savings Plans

An annuity is any sequence of periodic payments. If made at the end of each time interval, then it is an Ordinary Annuity. We will study only ordinary annuities in this course. The Future Value (FV) of an ordinary annuity is the sum of all payments plus interest earned.

A savings plan: Suppose you deposit $100 every six months into an account that pays 6% compounded semi-annually. If you make 6 deposits, one at the end of each interest payment period, over 3 years, how much money will be in the account after the last deposit is made?

Example: In order to accumulate enough money for a down payment on a home, a couple deposits $300 per month into an account paying 6% compounded monthly. If payments are made at the end of each period, how much money will be in the account in 5 years?

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Example: A person wishes to have $200,000 in an account for retirement 15 years from now. How much money should be deposited quarterly in an account paying 8% compounded quarterly? Note: Sometimes this is called a "sinking fund".

Total and Annual Return: Total Return = FV - P P

1

Annual Return = A Y -1 P

The Annual Return is the average annual percentage yield that gives the same overall growth.

Example: David invested $5,000 into Sonic Solutions (SNIC on the NASDAQ exchange). Five years later his investment grew to 32,000. Determine the total and annual returns for the 5-year period.

Note: Investment loss can be handled in a similar manner.

Your turn! Types of Investment: Students read p 198-223. Understand the 3 basic types of investment: stocks, bonds, and cash. Please work through the examples given on these pages and the associated suggested exercises. If you have any questions, please ask!

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