Question

PRESENT VALUE OF AN ANNUITY

Find the present values of these ordinary annuities. Discounting occurs once a year. Round your answers to the nearest cent.

1. $600 per year for 16 years at 12%.

   $  

2. $300 per year for 8 years at 6%.

   $  

3. $900 per year for 16 years at 0%.

   $  

   Rework previous parts assuming that they are annuities due. Round your answers to the nearest cent.

4. $600 per year for 16 years at 12%.

   $  

5. $300 per year for 8 years at 6%.

   $  

6. $900 per year for 16 years at 0%.

   $  

Answer 1

a. Present Value = $ 600 * 1/(1.12) ^ 1 +$ 600 * 1/(1.12) ^2 +$ 600 * 1/(1.12) ^3+.... + $ 600 * 1/(1.12) ^16

= $ 4,184.39

Hence the correct answer is $ 4,184.39

b. Present Value = $ 300 * 1/(1.06) ^ 1 +$ 300 * 1/(1.06) ^2+$ 300 * 1/(1.06) ^3+$ 300 * 1/(1.06) ^4+$ 300 * 1/(1.06) ^5+$ 300 * 1/(1.06) ^6+$ 300 * 1/(1.06) ^7+$ 300 * 1/(1.06) ^8

= $ 1,862.94

Hence the correct answer is $ 1,862.94

c. Present Value = 900 * 1/(1.0) ^ 1 + 900 * 1/(1.0) ^ 2+900 * 1/(1.0) ^ 3+.... +900 * 1/(1.0) ^ 16

= $ 14,400

Hence the correct answer is $ 14,400

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

= $ 4,184.39 * ( 1+12/100)

= $ 4,686.5168

= $ 4,686.52

Hence the correct answer is $ 4,686.52

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

= $ 1,862.94 * ( 1.06)

= $ 1,974.72

Hence the correct answer is $ 1,974.72

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

= $ 14,400 * (1+0%)

= $ 14,400

Hence the correct answer is $ 14,400