# Annuities Compound Interest

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```					Compound Interest and Annuities

Assumptions:
r                10%   Annually

Mths            PV       Interest   Mthly Pmt          FV
1     \$     -      \$       -            200   \$     200
2     \$     200    \$      1.67          200   \$     402
3     \$     402    \$      3.35          200   \$     605
4     \$     605    \$      5.04          200   \$     810
5     \$     810    \$      6.75          200   \$   1,017
6     \$   1,017    \$      8.47          200   \$   1,225
7     \$   1,225    \$    10.21           200   \$   1,435
8     \$   1,435    \$    11.96           200   \$   1,647
9     \$   1,647    \$    13.73           200   \$   1,861
10     \$   1,861    \$    15.51           200   \$   2,077
11     \$   2,077    \$    17.31           200   \$   2,294
12     \$   2,294    \$    19.12           200   \$   2,513
13     \$   2,513    \$    20.94           200   \$   2,734
14     \$   2,734    \$    22.78           200   \$   2,957
15     \$   2,957    \$    24.64           200   \$   3,181
16     \$   3,181    \$    26.51           200   \$   3,408
17     \$   3,408    \$    28.40           200   \$   3,636
18     \$   3,636    \$    30.30           200   \$   3,867
19     \$   3,867    \$    32.22           200   \$   4,099
20     \$   4,099    \$    34.16           200   \$   4,333
21     \$   4,333    \$    36.11           200   \$   4,569
22     \$   4,569    \$    38.08           200   \$   4,807
23     \$   4,807    \$    40.06           200   \$   5,047
24     \$   5,047    \$    42.06           200   \$   5,289
Compound Interest and Annuities
Formula:      FV  PV (1  i) nt                           Formula II: Annuity (periodic deposits)

FV - Future Value                                                      (1  i ) nt  1 
PV - Present Value                                              FV  P
                 

r - annual interest rate                                                      i        
i = period interest rate = r/n
t - years                                                  P = periodic deposit
n = number of periods per year (usually months)

How to become a Millionaire (using formula II)

Begin saving at Age         Balance at age           Actual
(np)                    60 (FV)         Contribution
Assumptions:                                                       60                              \$0               \$0
55                        \$15,487          \$12,000
PV             \$    -                                              50                        \$40,969          \$24,000
ir (annual)         10%                                            45                        \$82,894          \$36,000
pmt (mthly)          200                                           40                       \$151,874          \$48,000
35                       \$265,367          \$60,000
30                       \$452,098          \$72,000
25                       \$759,328          \$84,000
20                     \$1,264,816          \$96,000
Example:

What would the value be the value of an annuity of 200 per month that returns 8% annually for 5 years.
Assume monthly compounding of interest.

 (1  i ) nt  1                                   Using Excel Function
FV  P
                 
   =        \$14,695.37               (\$14,695.37)      Considered an outflow of money
        i        
Quiz Problem:
What would the value be the value of an annuity of 100 per month that returns 15% annually for 10 years.
Assume monthly compounding of interest.
Compound Interest and Annities
With Variable Monthly Payment Amount

Assumptions:

PV         \$     100
ir               10%   Annually

Age       Year           PV   Mthly Pmt           FV Your Contribution
21          1     \$     100          50         \$739               600
22          2     \$     739          50       \$1,444             1,200
23          3     \$ 1,444            50       \$2,224             1,800
24          4     \$ 2,224            50       \$3,085             2,400
25          5     \$ 3,085            50       \$4,036             3,000
26          6     \$ 4,036           100       \$5,716             4,200
27          7     \$ 5,716           100       \$7,571             5,400
28          8     \$ 7,571           100       \$9,620             6,600
29          9     \$ 9,620           100      \$11,884             7,800
30         10     \$ 11,884          100      \$14,385             9,000
31         11     \$ 14,385          200      \$18,404            11,400
32         12     \$ 18,404          200      \$22,844            13,800
33         13     \$ 22,844          200      \$27,750            16,200
34         14     \$ 27,750          200      \$33,169            18,600
35         15     \$ 33,169          200      \$39,155            21,000
36         16     \$ 39,155          400      \$48,281            25,800
37         17     \$ 48,281          400      \$58,363            30,600
38         18     \$ 58,363          400      \$69,501            35,400
39         19     \$ 69,501          400      \$81,804            40,200
40         20     \$ 81,804          400      \$95,397            45,000
41         21     \$ 95,397          500     \$111,669            51,000
42         22     \$ 111,669         500     \$129,645            57,000
43         23     \$ 129,645         500     \$149,503            63,000
44         24     \$ 149,503         500     \$171,441            69,000
45         25     \$ 171,441         500     \$195,676            75,000
46         26     \$ 195,676         500     \$222,448            81,000
47         27     \$ 222,448         500     \$252,024            87,000
48         28     \$ 252,024         500     \$284,697            93,000
49         29     \$ 284,697         500     \$320,791            99,000
50         30     \$ 320,791         500     \$360,665          105,000
51         31     \$ 360,665         500     \$404,714          111,000
52         32     \$ 404,714         500     \$453,376          117,000
53         33     \$ 453,376         500     \$507,133          123,000
54         34     \$ 507,133         500     \$566,520          129,000
55         35     \$ 566,520         500     \$632,124          135,000
56         36     \$ 632,124         500     \$704,599          141,000
57         37     \$ 704,599         500     \$784,662          147,000
58         38     \$ 784,662         500     \$873,109          153,000
59         39     \$ 873,109         500     \$970,818          159,000
60         40     \$ 970,818         500   \$1,078,758          165,000

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