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5 MATHEMATICS OF FINANCE
Copyright © Cengage Learning. All rights reserved.
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5.3 Amortization and Sinking Funds
Copyright © Cengage Learning. All rights reserved.
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Sinking Funds
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Sinking Funds Sinking funds are another important application of the annuity formulas. Simply stated, a sinking fund is an account that is set up for a specific purpose at some future date. For example, an individual might establish a sinking fund for the purpose of discharging a debt at a future date. A corporation might establish a sinking fund in order to accumulate sufficient capital to replace equipment that is expected to be obsolete at some future date.
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Applied Example 7 – Sinking Fund
The proprietor of Carson Hardware has decided to set up a sinking fund for the purpose of purchasing a truck in 2 years’ time. It is expected that the truck will cost $30,000. If the fund earns 10% interest per year compounded quarterly, determine the size of each (equal) quarterly installment the proprietor should pay into the fund. Verify the result by displaying the schedule.
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Applied Example 7 – Solution
The problem at hand is to find the size of each quarterly payment R of an annuity, given that its future value is S = 30,000, the interest earned per conversion period is 𝑟 𝑚 = =0.025, and the number of payments is n = (2)(4) = 8. The formula for an annuity, 𝑆=𝑅 𝑟 𝑚 𝑛 −1 𝑟 𝑚
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Applied Example 7 – Solution
cont’d When solved for R yields 𝑅= 𝑟 𝑚 ∙𝑆 1+ 𝑟 𝑚 𝑛 −1 (14)
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Applied Example 7 – Solution
cont’d Substituting the appropriate numerical values for 𝑟 𝑚 , S, and n into Equation (14), we obtain the desired quarterly payment or $
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Applied Example 7 – Solution
cont’d Table 5 shows the required schedule. Table 5
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Sinking Funds The formula derived in this last example is restated as follows. 𝑟 𝑚 𝑅= 𝑟 𝑚 ∙𝑆 1+ 𝑟 𝑚 𝑛 −1
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Sinking Funds Here is a summary of the formulas developed are as follows 1. Simple and compound interest; annuities 𝑟 𝑚 𝑟 𝑚 𝑟 𝑚 𝑟 𝑚
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Sinking Funds 2. Effective rate of interest 3. Amortization
∙ 𝑟 𝑚 Periodic payment 𝑟 𝑚 𝑟 𝑚 Amount amortized
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Sinking Funds 4. Sinking fund 𝑟 𝑚 ∙ Periodic payment taken out 𝑟 𝑚
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Practice p. 304 #9, 27
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