# Future Value of Annuity Due with Different Percent Rate

Basically I understand how to solve a FVA problem if its just one static interests rate (%) and this is the Formula I use.

But this table from Bank's Rate Table is confusing me on how to calculate FVA since the rate is changing according to the sum value of saving.

Example :

Let say, I like to put \$100,000 at the beginning of every year for 20 years.

This is my calculation for year 1 with 0.65% interests (according rate in the table).

``````= 100000 [(1+0.0065)^1-1/0.0065](1+0.0065)
= 100000 [0.0065/0.0065](1.0065)
= 100000 (1)(1.0065)
= (100000)(1.0065)
t1 = \$100,650.00 (for first year)
``````

and year 2 with 1.10% interests rate (also rate in the table) since the amount from year 1 is above \$100k.

``````= 100650 [(1+0.011)^1-1]/0.011](1+0.011)
= 100650 [0.011/0.011](1.0110)
= 100650 (1)(1.0110)
= (100650)(1.0110)
t2 = 101,757.15 (2nd year)
``````

Is this approach correct?

and how do I move to 3rd year? Do I need to add t1+t2?

Thanks.

## 1 Answer

The way I read this question is that it is a tiered interest rate account. So you need to split the total amount invested each year into the tiers and calculate simple interest on this for the year. It gets complicated - banking details - if you're investing only a part of the year but your example assumes full years.

So in any year first 10,000 (first two tiers) earns 0.3% (result 30), next 15,000 (25,000 next band limit minus the 10,000 already used) earns 0.35%, next 25,000 earns 0.40%, etc. For year 1 I get 507.50 interest (3 + 27 + 52.5 + 100 + 325 for each tier) Apply this for every future year where you start with the amount calculated at the end of the prior year plus a new deposit of 100,000.

A single formula is quite a challenge on this case. Just build it as a loop in Excel or something similar.

• I see, thanks. I tried to google but I can't find the corrects terms for this problem. All the example showing only single value of interests and not multiple tiers like this. Still confusing me thou.. Nov 21, 2018 at 3:01