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Section 4B Savings Plans and Investments Pages 227-250

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Savings Plans and Investments The Savings Plan Formula Planning Ahead with Savings Plans Total and Annual Returns Types of Investments Stocks Bonds Mutual Funds

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Savings Plans Deposit a lump sum of money and let it grow through the power of compounding (4A). Deposit smaller amounts [in an interest earning account] on a regular basis (4B) IRA’s, 401(K), Koegh, Pension Special Tax Treatment

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You deposit $100 into a savings plan at the end of each month. The plan has an APR of 12% and pays interest monthly. End of... Prior balance Interest on Prior Balance End of month deposit New Balance Month 1 00$100 Month2$100.01x100 = $1 $100$201 Month 3$201.01x201 =$2.01 $100$303.01 Month4$303.01.01x303.01 =$3.03 $100$406.04 Month5$406.04.01x406.04 =$4.06 $100$510.10 Month6$510.10.01x510.10 =$5.10 $100$615.20

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Is there a Savings Plan Formula? where A = accumulated savings plan balance PMT = regular payment amount APR = annual percentage rate (decimal) n = number of payment periods per year Y = number of years This formula assumes the same payment and compounding periods. WOW !!!

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Where did this formula come from? Another way to figure accumulated value. End of month1 payment is now worth $100 x (1.01) 5 End of month2 payment is now worth $100 x (1.01) 4 End of month3 payment is now worth $100 x (1.01) 3 End of month4 payment is now worth $100 x (1.01) 2 End of month5 payment is now worth $100 x (1.01) 1 End of month6 payment is now worth $100 After 6 months:

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100 x (1.01) 5 +100 x (1.01) 4 +100 x (1.01) 3 +100 x (1.01) 2 +100 x (1.01) 1 +100 = $100 x ((1.01) 5 + (1.01) 4 + (1.01) 3 + (1.01) 2 + (1.01) + 1) Do you see a pattern? After 10 months: A = 100 x ((1.01) 9 + (1.01) 8 + (1.01) 7 + … + (1.01) 2 + (1.01) + 1) After 55 months: A = 100 x ((1.01) 54 + (1.01) 53 + (1.01) 52 + … + (1.01) 2 + (1.01) + 1) Where did this formula come from?

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After N months: A = $100 x [(1.01) N-1 + (1.01) N-2 + (1.01) N-3 + … + (1.01) 2 + (1.01) + 1] Where did this formula come from?

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Use the savings plan formula to calculate the balance after 6 months for an APR of 12% and monthly payments of $100. Calculator:

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At age 30, Michelle starts an IRA to save for retirement. She deposits $100 at the end of each month. If she can count on an APR of 8%, how much will she have when she retires 35 years later at age 65? Compare the IRA’s value to her total deposits over this time period. Calculator:

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At age 30, Michelle starts an IRA to save for retirement. She deposits $100 at the end of each month. If she can count on an APR of 8%, how much will she have when she retires 35 years later at age 65? Compare the IRA’s value to her total deposits over this time period.

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The accumulated value of the IRA is $229,388 The value of the deposits is 35 x 12 x 100 = $42,000 [Compounding interest accounts for $229,388 - $42,000 = $187,388.] The Power of Compounding WOW!

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(Planning Ahead with Savings) You want to build a $100,000 college fund in 18 years by making regular, end of the month deposits. Assuming an APR of 7%, calculate how much you should deposit monthly. How much of the final value comes from actual deposits and how much from interest?

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The monthly payments are $232.17. The value of the deposits is 18 x 12 x $232.18 = $50,148.72 [The accumulated value of the fund is $100,000.] [Compounding interest accounts for $100,000 - $50,148.72 = $49,851.28.] WOW! The Power of Compounding

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More Practice Find the savings plan balance after 18 months with an APR of 6% and monthly payments of $200.

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More Practice You set up an IRA with an APR of 5% at age 25. At the end of each month you deposit $50 in the account. How much will the IRA contain when you retire at age 65? Compare the amount to the total amount of deposits made over the time period.

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More Practice You intend to create a college fund for your baby. If you can get an APR of 7.5% and want the fund to have a value of $150,000 after 18 years, how much should you deposit monthly?

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More Practice You intend to create a college fund for your baby. If you can get an APR of 7.5% and want the fund to have a value of $150,000 after 18 years, how much should you deposit monthly?

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Homework Pages 245-250 # 38, 40, 45, 46

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Copyright © 2011 Pearson Education, Inc. Managing Your Money.

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