In Part 1 of this article, we developed a number of formulas for DNI for investment plans that return your deposit at the end of the investment term.  In this second part of the article, I’ll try to come up with a few formulas for DNI for investment plans that return your deposit as part of your earnings.  As we did for the plans we looked at in Part 1, we will also develop separate formulas for plans where interest is paid on calendar days and where it is paid on business days.

Before I begin, it would be a good idea to recall the symbols and their meanings that were introduced in Part 1.  Here they are:

DNI = daily net interest (based on calendar days)

DNIB = daily net interest (based on business days)

TNI = total net interest

DGI = daily gross interest

TGI = total gross interest

CD = calendar days

With this out of the way, let’s begin…

Deposit Included with Your Earnings — Interest Paid on Calendar Days

When your deposit is included with your earnings, your daily interest return is called a GROSS return because it isn’t all profit.  DGI is the symbol we use for that.  OK, let’s take a look at an investment plan that includes your deposit with your earnings.  Your total gross earnings for the plan over its entire term would be your daily gross earnings times the number of days in the plan or,

TGI = DGI x CD

Since this includes your investment, we subtract 100% from it to get the total NET interest that you earn or,

TNI = DGI x CD – 100

Finally, since your daily net interest, DNI, is the AVERAGE profit per day over the investment plan, you can obtain it by dividing the total net interest by the number of days in the investment term to get:

DNI = (DGI x CD – 100)/CD     FORMULA #4

Example 4.

An investment plan pays you 4.2% daily interest for 40 days.  What is the DNI of the plan?

The terms that we will use in Formula #4 are:

DGI = 4.2%

CD = 40

Substituting into Formula #4, we get:

DNI = (4.2 x 40 – 100)/40 = 1.70%

If your earnings are paid only on business days, then your total gross interest will be DGI x BD instead of DGI x CD.  To get your total NET interest, like the previous case, you would subtract 100 from the gross to get:

TNI = DGI x BD -100

To get DNI, we are looking at the net interest averaged over the CALENDAR days in the investment plan.  So, we divide the previous result by the number of calendar days to get:

DNI = (DGI x BD – 100)/CD     FORMULA #5

If you know the number of calendar days in the investment plan, you can use this formula to get the DNI.  However, typically, you are given the number of business days.  Well, no problem, because in Part 1 of the article we determined that CD = 1.36 BD.  Substituting this into the previous result, you finally get:

DNI = (DGI x BD – 100)/(1.36 BD)     FORMULA #5a

Example 5.

Find the DNI for an investment plan that pays 3.2% interest on business days for 90 business days.

The values for the terms in Formula #5a are:

DGI = 3.2

BD = 90

Substituting these values into Formula #5a, we get:

DNI = (3.2 x 90 – 100)/(1.36 x 90) = 1.54%

Summary of Formulas for DNI for Investment Plans that Return Your Deposit as Part of Your Earnings.

Interest Paid on Calendar Days

DNI = (DGI x CD – 100)/CD     FORMULA #4

DNI = (DGI x BD – 100)/CD     FORMULA #5

DNI = (DGI x BD – 100)/(1.36 BD)     FORMULA #5a

OK, that’s about if for DNI Formulas.  As we suggested in Part 1 of this article, you might want to copy these formulas down on a piece of paper and keep them in a handy spot.  You will find that, once you get used to using them, you will be able to come up with the DNI for just about any investment plan that you might encounter in just a minute or two.  You won’t need me to do this for you anymore!

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