Question

Find the present values of these ordinary annuities. Discounting occurs once a year. Do not round intermediate calculations. Round your answers to the nearest cent.

a.) $700 per year for 14 years at 10%.

b.)$350 per year for 7 years at 5%.

c.)$700 per year for 7 years at 0%.

Rework previous parts assuming they are annuities due.

a.)Present value of $700 per year for 14 years at 10%:

b.)Present value of $350 per year for 7 years at 5%:

c.)Present value of $700 per year for 7 years at 0%: Please explain it

Please explain it

Answer 1

Solution :-

Ordinary Annuity :- Annuity that begin immediately , means we say in the beginning of the year

(a) Present Value = $700 + $700 * PVAF( 10% , 13 )

= $700 + $700 * [ 1 - (1 + 0.10)^-13 ] / 0.10

= $700 + $7000 * [ 1 - 0.2897 ]

= $700 + $4,972.35

= $5,672.35

(b) Present Value = $350 + $350 * PVAF( 5% , 6 )

= $350 + $350 * [ 1 - (1 + 0.05)^-6 ] / 0.05

= $350 + $7,000 * [ 1 - 0.7462 ]

= $2,126.49

(C) Present Value ( in case of 0% Interest Rate ) = Cash flow * Life

= $700 * 7

= $4,900

Annuity Due :- Annuity Due is just a annuity in which the annuity occurs at the end of the year

(a) Present Value = $700 * PVAF( 10% , 14 )

= $700 * [ 1 - (1 + 0.10)^-14 ] / 0.10

= $7000 * [ 1 - 0.2633 ]

= $5,1,56.68

(b) Present Value = $350 * PVAF( 5% , 7 )

= $350 * [ 1 - (1 + 0.05)^-7 ] / 0.05

= $7,000 * [ 1 - 0.7107 ]

= $2,025.23

(C) Present Value ( in case of 0% Interest Rate ) = Cash flow * Life

= $700 * 7

= $4,900

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