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Microeconomics and Macroeconomics FCS 3450 Spring 2015 Unit 3

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What is future value? Accumulated amount of your investment fund. P = principle (original invested amount) r = interest rate for a certain period n = number of periods In this calculation, all periods have to be the same. Concept 8: Future Value (FV)

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Simple Interest vs. Compounding Interest Simple interest means you receive interest on original amount invested only. Compound interest means you receive interest on both the original amount invested and the interest rate you made from the investment (interest on interest).

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Effect of Compound Interest

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The Difference Between Simple Interest and Compound Interest Simple Interest is the interest computed on principal only Interest = Principle x Rate x Time or I = P x R x T. Compound Interest is the calculation of interest on interest as well as interest on the original investment.

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Future Value for One-Time Investment

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Rule of 72 A handy formula to calculate the number of years it takes to double principal using compound interest is the Rule of 72. You simply divide the interest rate the money will earn into the number 72. For example, if interest is compounded at a rate of 7 % per year, your principle will double every 10.3 years. If the rate is 6 %, it will take 12 years.The rule of 72 also works for determining how long it would take for the price of something to double given a rate of increase in the price. For example, if college tuition costs are rising 8 % per year, the cost of college education doubles in just over nine years.

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Future Value Example You put $10,000 in a CD account for 2 years. The account pays 4% annual interest. How much money will you have at the end if annual compounding interest is used? How about monthly compounding? How about daily compounding?

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Future Value Calculations Annual compounding: FV = $10,000 * (1+4%)^2 = $10,000 x 1.08160 = $10,816.00 Monthly compounding: (monthly interest rate = 4%/12 = 0.3333 %; n=2*12 = 24 FV = $10,000 * (1+0.3333%) ^24 = $10,000 x 1.083134 = $10,831.34 Daily compounding: (daily interest rate – 4%/365 = 0.0110%, n = 2*365 = 730 FV = $10,000 * (1+.0110%)^730 = $10,000 * 1.083607 = $10,836.07

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FV of Periodical Investments (Annuity) Periodical investments, or annuities, are multiple investments that are made at certain time intervals (every day, month, year, etc.)

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Example of Periodic Investment Suppose you have decided to save some money for a vacation. You can afford to save $100 month. You believe you can earn 8% on your money, compounded monthly. How much money will you have at the end of the 12 th month?

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Applying FVA calculation

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FVA Calculation FVA = Pp * FVFS Where Pp = amount of periodic payments

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Future Value Factor of an Annuity (FVA)

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Future Value of a Dollar (Single Payment)

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Future Value of a Series of Annual Deposits (Annuity)

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Present Value of a Dollar (Single Payment)

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Present Value of a Series of Annual Deposits (Annuity)

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Do I have the money now? Yes No Is it a lump sum? Is it a lump sum? Yes No Use FV Use Future Value Table Use PVUse PVA Keeping the Time Value of Money Formulas Straight Use FVA Use Present Value Table

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The Time Value of Money in Decision Making Assume you have the option of two different investment options. First, a friend wanted to borrow $5,000 for three years and pay you back $6,000 in a lump sum. Second, you could invest the same $5,000 for three years in a government bond paying 7 percent annual interest. Which investment would be the best financial decision? FV = (PV)(1 + r) n = (5,000)(1+.07) 3 = 5,000 x 1.225043 = $6,125.22 You would earn $125.22 more by investing in the government bonds.

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