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**Savings Goals and Institutions. Saving options, features and plans.**

Chapter 10 Saving for the future Savings Goals and Institutions. Saving options, features and plans.

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**Lesson 10.1 Savings Goals and Institutions**

Describe different purposes of saving. Explain how money grows through compounding interest. List and describe the financial institutions where you can save.

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**Why You Should Save Short-term needs Long-term needs**

Home ownership Education Retirement Investing Financial security

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**Where You Can Save Commercial banks Savings banks**

Savings and loan associations Credit unions Brokerage firms

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**Saving Options Regular savings account High liquidity Lower interest**

Free to make withdrawals and deposits Service fees may apply Can use ATM/Debit cards

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**Saving Options Certificate of Deposit (CD)**

Earns a fixed interest rate for a specified length of time Requires a minimum deposit Higher interest rate then regular savings Must leave money in for the entire time Has a set maturity date-the date the investment becomes due for payment

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**Saving Options Money market account**

Combination savings-investment plan Interest rates go up and down with the stock market Money is used to purchase safe, liquid securities Offered by banks and brokerage firms Money can be deposited/withdrawn at any time with no fee Usually not insured

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**Selecting a Savings Plan**

Factors to consider Liquidity Safety Convenience Interest-Earning potential (Yield) Fees and Restrictions

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**Saving Regularly Ways to Save Must spend less money than you take in**

Direct Deposit Automatic Payroll Deductions

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Types of Interest Interest is based on interest rate and principal (balance) Simple interest is calculated on principal only Compound interest is money earned on the money deposited plus previous interest

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Simple Interest

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**Example 1 Simple interest**

Grace wants to deposit $5000 in a certificate of deposit for a period of two years. She is comparing interest rates quoted by three local banks and one online bank. Write the interest rates in ascending order. Which bank pays the highest interest for this two-year CD?

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**Example 1 continued First State Bank: E-Save Bank:**

Johnson City Trust: 4.22% Land Savings Bank: 4.3%

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**Simple Interest example 2**

Raoul’s Savings account must have at least $500, or he is charged a $4 fee. His balance was $716.23, when he withdrew $225. Will he be charged a fee?

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**Simple Interest Example 3**

Mitchell deposits $1200 in an account that pays 4.5% simple interest. He keeps the money in the account for three years. How much is in the account after three years?

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**Simple Interest Example 4**

How much simple interest does $200 earn in 7 months at an interest rate of 5%

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**Simple Interest Example 5**

How much principal must be deposited to earn $1000 simple interest in 2 years at a rate of 5%?

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**Simple Interest Example 6**

Derek has a bank account that pays 4.1% simple interest. The balance is $910. When will the account grow to $1000?

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**Simple Interest Example 7**

Kerry invests $5000 in a simple interest account for 5 years. What interest rate must the account pay so there is $6000 at the end of 5 years?

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**Compound Interest Terms**

Annual compounding-once each year Semiannual Compounding-twice a year Quarterly compounding-4 times a year Daily compounding-365 times a year (366 in a leap year)

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Example 1 How much interest would $1000 earn in one year at a rate of 6%, compounded annually? What would be the new balance?

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Example 2 Maria deposits $1000 in a savings account that pays 6% interest, compounded semiannually. What is her balance after one year?

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Example 3 How much interest does $1000 earn in three months at an interest rate of 6%, compounded quarterly? What is the balance after three months?

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Example 4 How much interest does $1000 earn in one day at an interest rate of 6%, compounded daily? What is the balance after one day?

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**Compound Interest Formula**

B=ending balance p=principal r=interest rate N=number of times interest is compounded annually T=number of years

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Example 1 Marie deposits $1650 for three years at 3% interest, compounded daily. What is her ending balance?

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Example 2 Kate deposits $2350 in an account that earns interest at a rate of 3.1%, compounded monthly. What is her ending balance after five years?

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**APY/APR APR-annual percentage rate APY-annual percentage yield**

Banks usually advertise Higher than APR for accounts compounded more than once per year

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**Annual percentage yield formula**

r= interest rate N=number of times per year

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Example 1 Sharon deposits $8000 in a one year CD at 3.2% interest, compounded daily. What is Sharon’s annual percentage yield (APY) to the nearest hundredth of a percent?

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Example 2 Barbara deposits $3000 in a one year CD at 4.1% interest, compounded daily. What is the APY to the nearest hundredth of a percent?

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**Continuous Interest B=ending balance P=principal**

E=exponential base (on Calc) r=interest rate t=number of years

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Example 1 Craig deposits $5000 at 5.12% interest, compounded continuously for four years. What would his ending balance be to the nearest cent?

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Example 2 If you deposit $1000 at 4.3% interest, compounded continuously, what would your ending balance be to the nearest cent after five years?

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**Future value of a periodic deposit investment**

Periodic investments are the same deposits made at regular intervals such as yearly, monthly, biweekly, etc.

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**Future Value Of A Periodic Deposit**

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Example 1 Rich and Laura are both 45 years old. They want to retire at age 65. They deposit $5000 each year into an account that pays 4.5% interest, compounded annually. What is the account balance when they retire?

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Example 1 con’t How much interest will Rich and Laura earn over the 20-year period?

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Example 2 Linda and Rob open an online savings account that has a 3.6% annual interest rate, compounded monthly. If they deposit $1200 every month, how much will be in the account after 10 years?

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**Present Value Of A Single Deposit**

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Example 1 A mom knows that in 6 years, her daughter will attend College. She will need about$20,000 for the first year’s tuition. How much should the mom deposit into an account that yields 5% interest, compounded annually?

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Example 2 Ritika just grauated from college. She wants $100,000 in her savings account after 10 years. How much must she deposit in that account now at a 3.8% interest rate, compounded daily, in order to meet that goal?

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**Present Value Of A Periodic Deposit**

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Example 1 Nick wants to install central air conditioning in his home in 3 years. He estimates the total cost to be $ How much must he deposit monthly into an account that pays 4% interest, compounded monthly, in order to have enough money?

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Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 1 3-5 COMPOUND INTEREST FORMULA Become familiar with the derivation of the compound.

Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 1 3-5 COMPOUND INTEREST FORMULA Become familiar with the derivation of the compound.

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