Math 325 Ch 4 (4.2, 4.4, 4.5) – More General Annuities
We'll discuss annuities for which the payments are made more or less frequently than the interest is convertible and for which payments vary in size (non-level payments).
To find the value of an annuity in which payment and interest conversion periods differ and payments are level, the key is to find the rate of interest, convertible at the same frequency as payments are made, that is equivalent to the given interest rate.
Example 1 . Find the accumulated value at the end of 4 years of an investment fund in which $100 is deposited at the beginning of each quarter for the first 2 years and $200 is deposited at the beginning of each quarter for the next 2 years, if the fund earns 12%, convertible monthly.
NOTE: SKIP Section 4.3 of the book.
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Math 325 Ch 4 (4.2, 4.4, 4.5) – More General Annuities
M-thly Payble Annuities
Suppose we have an annuity with n interest conversion periods, and m payments made during each conversion period. Then, n is the term of the annuity measured in interest conversion periods, and there are mn total payments made.
For example, A 10-year annuity with annual payments of $1200 payable monthly means that you receive $100 per month for 120 months.
In this example, n = 10 with m = 12. Assuming an annual effective rate i , the PV of this annuity is denoted by
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Math 325 Ch 4 (4.2, 4.4, 4.5) – More General Annuities
Example 2 . Ted secures a loan that requires him to pay $800 at the end of each month for 15 years. IF the annual effective interest rate is 4.25%, what is the amount of the loan?
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Math 325 Ch 4 (4.2, 4.4, 4.5) – More General Annuities
Example 3 . At what annual effective rate of interest is the PV of annual payments of $60 payable quarterly forever, with the first payment made immediately, equal to $750.
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Math 325 Ch 4 (4.2, 4.4, 4.5) – More General Annuities
Continuous Annuities
An annuity for which the frequency of payment is infinite.
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Math 325 Ch 4 (4.2, 4.4, 4.5) – More General Annuities
Example 4 . Payments of $1200 per year are made continuously over a 7-year period. Find the accumulated value of this fund two years after the payments end, assuming interest is 9% per year compounded continuously.
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