Question

PRESENT VALUE OF AN ANNUITY Find the present values of these ordinary annuities. Discounting occurs once a year. 1. $600 per year for 12 years at 8% 2. $300 per year for 6 years at 4% 3. $500 per year for 6 years at 0% 4. Rework parts a, b, and c assuming they are annuities due.

Answer 1

Answer:

    ordinary   // annnuity-due

1.- 4,521.65   //  4,883.38

2.- 1,572.64  //  1,635.54

4.- 3,000.00 //  3,000

Explanation:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 600.00

time 12

rate 0.08

$600 \times \frac{1-(1+0.08)^{-12} }{0.08} = PV$

PV $4,521.6468

Annuity-due

$600 \times \frac{1-(1+0.08)^{-12} }{0.08}(1+0.08) = PV$

PV $4,883.3786

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 300.00

time 6

rate 0.04

$300 \times \frac{1-(1+0.04)^{-6} }{0.04} = PV$

PV $1,572.6411

Annuity-due

1,572.6411 x 1.04 = $1,635.5467

4.- as interest rate is 0% the money do not lose value over time

will be 3,000 regardless of time or type of annuity