The Investment Year Method

The investment year method is a growth pattern in which the rate of interest applicable to an investment varies by year and depends on the time at which that investment was made. The rates are taken from a table, which might look something like this:

Year of Investment	Rate in Year 1	Rate in Year 2	Rate in Year 3	Rate in Year 4	First Ultimate Rate
2000	.06	.065	.0575	.06	.065
2001	.07	.0625	.06	.07	.0675
2002	.06	.06	.0725	.07	.0725
2003	.0775	.08	.08	.0775	.0715

To get the rates for an investment, you first identify the row using the leftmost column based on the year in which the investment was made, for each subsequent year, you move one column to the right until reaching the rightmost column. Each subsequent year after that, you move one column down.

For example, an investment made in the year 2000 and held for 7 years will have applicable rates of 6% in the first year, 6.5% in the second, 5.75% in the third, 6% in the fourth, 6.5% in the fifth, 6.75% in the sixth, and 7.25% in the seventh.

Examples

Suppose we invest 1,000 in the year 2000. If the rates in the above table represent annually compounded rates, how much does the investment grow to after 7 years?

Note that this method exhibits the same growth pattern as TmVal’s TieredTime class. We can use the function tt_iym() to read the above table if is in the form of a Python dictionary. The function parses the table based on the year of investment t0=2000, and then returns a TieredTime object. This object can then be passed to the Amount class along with the 1,000, which we can then use to calculate the answer.

In [1]: from tmval import Amount, tt_iym

In [2]: iym_table = {
   ...:  2000: [.06, .065, .0575, .06, .065],
   ...:  2001: [.07, .0625, .06, .07, .0675],
   ...:  2002: [.06, .06, .0725, .07, .0725],
   ...:  2003: [.0775, .08, .08, .0775, .0715]
   ...:  }
   ...: 

In [3]: tt = tt_iym(table=iym_table, t0=2000)

In [4]: amt = Amount(gr=tt, k=1000)

In [5]: print(amt.val(7))
1542.9665343418887