Question

Find the future value of the following annuities. The first payment in these annuities is made at the end of Year 1, so they are ordinary annuities. (Notes: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in many situations, to see how changes in input variables affect the output variable. Also, note that you can leave values in the TVM register, switch to Begin Mode, press FV, and find the FV of the annuity due.)

$800 per year for 10 years at 10%.

$400 per year for 5 years at 5%.

$800 per year for 5 years at 0%.

Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due.

Future value of $800 per year for 10 years at 10%:

Future value of $400 per year for 5 years at 5%:

Future value of $800 per year for 5 years at 0%:

Answer 1

FV of annuity

$800 per year for 10 years at 10%

Particulars	Amount
Cash Flow	800
Int Rate	10.000%
Periods	10

FV of Annuity = Cash Flow * [ [(1+r)^n ] - 1 ] /r
=800 * [ [(1+0.1)^10] - 1 ] / 0.1
=800 * [ [(1.1)^10] - 1 ] /0.1
=800 * [ [2.5937] - 1 ] / 0.1
=800 * [1.5937] /0.1
12749.94

$400 per year for 5 years at 5%.

Particulars	Amount
Cash Flow	400
Int Rate	5.000%
Periods	5

FV of Annuity = Cash Flow * [ [(1+r)^n ] - 1 ] /r
=400 * [ [(1+0.05)^5] - 1 ] / 0.05
=400 * [ [(1.05)^5] - 1 ] /0.05
=400 * [ [1.2763] - 1 ] / 0.05
=400 * [0.2763] /0.05
2210.25

$800 per year for 5 years at 0%.

At r = 0% , Present value = Future value

FV of annuity Due

$800 per year for 10 years at 10%

Particulars	Amount
Cash Flow	800
Int Rate	10.000%
Periods	10

FV of Annuity Due = Cash Flow * [ [(1+r)^(n+1) ] - 1 ] /r
=800 * [ [(1+0.1)^11] - 1 ] / 0.1
=800 * [ [(1.1)^11] - 1 ] /0.1
=800 * [ [2.8531] - 1 ] / 0.1
=800 * [1.8531] /0.1
14824.93

Future value anuity due of $400 per year for 5 years at 5%:

Particulars	Amount
Cash Flow	400
Int Rate	5.000%
Periods	5

FV of Annuity = Cash Flow * [ [(1+r)^(n+1) ] - 1 ] /r
=400 * [ [(1+0.05)^6] - 1 ] / 0.05
=400 * [ [(1.05)^6] - 1 ] /0.05
=400 * [ [1.3401] - 1 ] / 0.05
=400 * [0.3401] /0.05
2720.77

$800 per year for 5 years at 0%.

At r = 0% , Present value = Future value

Pls do rate, if the answer is correct and comment, if any further assistance is required.