1. 5 MATHEMATICS OF FINANCE
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2. 5.3 Amortization and Sinking Funds
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3. Sinking Funds

4. 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.

5. 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.

6. 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

7. Applied Example 7 – Solution
cont’d
When solved for R yields
𝑅= 𝑟 𝑚 ∙𝑆 1+ 𝑟 𝑚 𝑛 −1
(14)

8. 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 $

9. Applied Example 7 – Solution
cont’d
Table 5 shows the required schedule.
Table 5

10. Sinking Funds
The formula derived in this last example is restated as follows.
𝑟 𝑚
𝑅= 𝑟 𝑚 ∙𝑆 1+ 𝑟 𝑚 𝑛 −1

11. 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

12. Sinking Funds 2. Effective rate of interest 3. Amortization
∙ 𝑟 𝑚
Periodic payment
𝑟 𝑚
𝑟 𝑚
Amount amortized

13. Sinking Funds
4. Sinking fund
𝑟 𝑚 ∙
Periodic payment taken out
𝑟 𝑚

14. Practice
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