Question

$1 is paid at the end of every year for 50 years. Assume an interest rate of 5% unless otherwise noted.

3. Calculate the value of the annuity at t = 25 using the following methods:

1. Sum up the value of each individual payment

2. Use the annuity formulas

3. Use the excel formulas

4. Accumulate the value from part 1.1

5. Present value the value from part 2.1

For 4, part 1.1 gives total present value of $18.2559. And for 5, part 2.1 gives the total accumulated value of 209.3480 at t = 50.

Do this in excels please. And please show the equation that you using with the instructions given.

Answer 1

3)

Annuity =$ 1

t = 25 years

rate = 5%

1) Sum of the value of all individual payment is done excel

Year	Annuity	Present value of Annuity
1	1	0.95
2	1	0.91
3	1	0.86
4	1	0.82
5	1	0.78
6	1	0.75
7	1	0.71
8	1	0.68
9	1	0.64
10	1	0.61
11	1	0.58
12	1	0.56
13	1	0.53
14	1	0.51
15	1	0.48
16	1	0.46
17	1	0.44
18	1	0.42
19	1	0.40
20	1	0.38
21	1	0.36
22	1	0.34
23	1	0.33
24	1	0.31
25	1	0.30
		14.09

Present value of annuity in each year is calculated = Annuity / [1 + r%]^year

say PV of annuity in year 4 = 1 / [ 1 + 5%]⁴ => 0.82

To find PV of all annuities

= Summation of all present values of annuities in each year is done

Value of annuity by Sum up the value of each individual payment = $ 14.09

2)

Using Annuity formula

PV of annuity = P [ {1 - (1 + r) ^-n } / r]

here

P =$ 1

r =5%

n= 25

putting these values in the formula

PV = 1 [ {1 - ( 1 + 5%) ^-25 } / 5% ]

= { 1 - (1.05)^-25 } / .05

= [1 - 1 / 1.05²⁵] / 0.05

= [1 - 1 / 3.3863 ] / 0.05

= 0.07469 / 0.05

=> 14.09

3)

Using excel formula

Use Present Value(PV) function in excel

PV(Rate, nper, PMT,Fv,Type)

here,

Rate = 5%

nper = 25

PMT = -1

Type = 0 by default [ for payment at the end of the period]

=PV(5%,25,-1)

=> 14.09

All the above three methods yields the same result $ 14.09