Question

1. What is the present value of a $1,200 payment made in five years when the discount rate is 9 percent? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

2. What is the future value of a $1,000 annuity payment over four years if interest rates are 8 percent? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

3. What's the present value of a $930 annuity payment over five years if interest rates are 9 percent? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

4. Monica has decided that she wants to build enough retirement wealth that, if invested at 9 percent per year, will provide her with $5,100 of monthly income for 25 years. To date, she has saved nothing, but she still has 30 years until she retires. How much money does she need to contribute per month to reach her goal? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Please answer all of the questions, if you can not answer all of the questions do not reply.

Answer 1

1). PV = FV / (1 + r)ⁿ

= $1,200 / 1.09⁵ = $1,200 / 1.5386 = $779.92

2). FVA = Annuity x [{(1 + r)ⁿ - 1} / r]

= $1,000 x [{(1 + 0.08)⁴ - 1} / 0.08]

= $1,000 x [0.3605 / 0.08] = $1,000 x 4.50611 = $4,506.11

3). PVA = Annuity x [{1 - (1 + r)^-n} / r]

= $930 x [{1 - (1 + 0.09)^-5} / 0.09]

= $930 x [0.3501 / 0.09] = $930 x 3.8897 = $3,617.38

4). First, we need to find the PV of the desired monthly income at retirement,

PVA = Annuity x [{1 - (1 + r)^-n} / r]

= $5,100 x [{1 - (1 + 0.09/12)^-(25x12)} / (0.09/12)]

= $5,100 x [0.8937 / 0.0075] = $5,100 x 119.1616 = $607,724.27

Now, by taking this amount as the future value of annuity, we can calculate the value of monthly contribution

Annuity = [FVA x r] / [(1 + r)ⁿ - 1]

= [$607,724.27 x (0.09 / 12)] / [{1 + (0.09 / 12)}^(30x12) - 1]

= [$4,557.93 / 13.7306] = $331.95