Question

5.15

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. $1,000 per year for 10 years at 6%. $   $500 per year for 5 years at 3%. $   $200 per year for 5 years at 0%. $   Rework previous parts assuming they are annuities due. Present value of $1,000 per year for 10 years at 6%: $   Present value of $500 per year for 5 years at 3%: $   Present value of $200 per year for 5 years at 0%: $

Answer 1

a. Present Value = $ 1,000 * 1/ ( 1.06) ^ 1 +$ 1,000 * 1/ ( 1.06) ^2+$ 1,000 * 1/ ( 1.06) ^3+....$ 1,000 * 1/ ( 1.06) ^10

= $ 7,360.09

Hence the correct answer is $ 7,360.09

b. Present Value = $ 500 * 1/ ( 1.03) ^ 1 + $ 500 * 1/ ( 1.03) ^ 2+$ 500 * 1/ ( 1.03) ^ 3+....$ 500 * 1/ ( 1.03) ^ 5

= $ 2,289.85

Hence the correct answer is $ 2,289.85

c.

Present Value = $ 200 * 1/ ( 1.00) ^ 1 + $ 200 * 1/ ( 1.00) ^ 2+$ 200 * 1/ ( 1.00) ^ 3+$ 200 * 1/ ( 1.00) ^ 4+$ 200 * 1/ ( 1.00) ^ 5

= $ 1,000

Hence the correct answer is  $ 1,000

Annuity Due:

Present Value of Annuity Due = Present Value of Annuity * ( 1+ Rate of Interest)

Present value of $1,000 per year for 10 years at 6%:

7,360.09 * ( 1+6/100)

= $ 7,801.6954

= $ 7,801.70

Hence the correct answer is $ 7,801.70

Present value of $500 per year for 5 years at 3%:

2,289.85 * ( 1+3/100)

= 2358.5455

= $ 2,358.55

Hence the correct answer is $ 2,358.55

Present value of $200 per year for 5 years at 0%

=$ 1,000 * ( 1+0/100)

= $ 1,000

Hence the correct answer is $ 1,000