BUQU 1130 - Chapter 13.pptx - BUQU 1130 – Business Mathematics Chapter 13 ANNUITIES DUE DEFERRED ANNUITIES PERPETUITIES SHORA EBRAHIMI

BUQU 1130 - Chapter 13.pptx - BUQU 1130 – Business...

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BUQU 1130 – Business Mathematics Chapter 13 ANNUITIES DUE, DEFERRED ANNUITIES, PERPETUITIES SHORA EBRAHIMI SHORA [email protected]
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❶ Compute the future value, present value, periodic payment, term, and interest rate for simple annuities due ❷ Compute the future value, present value, periodic payment, term, and interest rate for general annuities due ❸ Compute the future value, present value, periodic payment, term, and interest rate for ordinary deferred annuities ❹ Compute the future value, present value, periodic payment, term, and interest rate for deferred annuities due ❺ Compute the present value, periodic payment, and interest rate for ordinary perpetuities, perpetuities due, and deferred perpetuities SHORA EBRAHIMI 2 Objectives BUQU 1130 - Chapter 13
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Simple Annuities Due If the periodic payment is made at the end of each payment interval the annuity is an ordinary annuity If the periodic payment is made at the beginning of each payment interval, the annuity is an annuity due SHORA EBRAHIMI 3 BUQU 1130 - Chapter 13
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Simple vs. Ordinary SHORA EBRAHIMI 4 BUQU 1130 - Chapter 13
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Simple Annuities Due - Future Value To calculate the future value of a simple annuity due The formula for the FV of an ordinary annuity is then multiplied by (1+i) to include the additional interest earned for the payment made at the beginning of the first period SHORA EBRAHIMI 5 BUQU 1130 - Chapter 13
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Simple Annuities Due - Future Value Formula: SHORA EBRAHIMI 6 ?? ? ( ??? ) = ??? [ ( 1 + ? ) ? 1 ? ] ( 1 + ? ) FV of Ordinary Simple Annuity Adjusted One Periods worth of Interest BUQU 1130 - Chapter 13
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Simple Annuities Due Due ” means that the payments are made at the beginning of the payment interval Simple ” means that the payment interval and interest conversion interval are the same. SHORA EBRAHIMI 7 BUQU 1130 - Chapter 13
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Let’s see an example Find the FV of $100 payments at 6% compounded annually made at beginning of the year for four years SHORA EBRAHIMI 8 $100 $100 $100 $100 Now-beginning of year 1 1 2 3 4 100(1+0.06) 4 100(1+0.06) 3 100(1+0.06) 2 100(1+0.06) 1 $106 $112.36 $119.10 $126.25 ?? = ??? ( ? . ?? ) ? + ??? ( ? . ?? ) ? + ??? ( ? . ?? ) ? + ??? ( ? . ?? ) ? = $ ??? . ?? BUQU 1130 - Chapter 13
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Let’s see an example Using the formula SHORA EBRAHIMI 9 ?? ? ( ??? ) = ??? [ ( 1 + ? ) ? 1 ? ] ( 1 + ? ) ?? 4 ( ??? ) = 100 [ ( 1 + 0.06 ) 4 1 0.06 ] ( 1 + 0.06 ) ?? 4 ( ??? ) = 100 [ ( 1.06 ) 4 1 0.06 ] ( 1.06 ) ?? 4 ( ??? ) = 100 ( 4.637093 ) = $ ??? . ?? BUQU 1130 - Chapter 13
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Let’s see an example How much interest is earned? Four payments of $100 $400 FV of the Ordinary Simple Annuity is $463.71 Interest earned: 463.71 – 400 = $63.71 SHORA EBRAHIMI 10 BUQU 1130 - Chapter 13
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Simple Annuities Due - Present Value Start with the present value formula for an ordinary annuity The formula is then adjusted to accommodate the difference in the timing of the payment by multiplying by the factor (1+ i ) SHORA EBRAHIMI 11 BUQU 1130 - Chapter 13
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Simple Annuities Due - Present Value Formula: SHORA EBRAHIMI 12 ??
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