HOW TO CALCULATE INTEREST IN 360-DAY AND 365-DAY YEARS

A fundamentally important task for treasurers is to oversee the organisation’s cash flow and shorter-term investments.

To do this successfully, the treasurer must:

  • Understand the cash flows from investments; and
  • Be able to compare different investment products consistently.

FIRST THINGS FIRST

Essential considerations for short-term investment are safety, liquidity and yield, in that order. Once safety (or ‘security’) and liquidity are satisfied,we can move on to compare yields.

This article focuses on calculating and applying yields. These are essential foundations for making valid comparisons.

HAPPY RETURNS

Say we invest 3,000,000 units of our local currency for a 90-day period, expecting to get back 3,030,000 at the end. The gain, surplus or interest is the difference between the amount at the end and the amount at the start.

In this case it will be 3,030,000 – 3,000,000 = 30,000.

YIELD APPEAL

To make returns comparable, gains are generally expressed as a percentage interest rate, also known as ‘yield’.

The gain of 30,000 on the starting amount of 3,000,000 represents a yield (r) of:
(r) = Gain / Starting amount

= 30,000 / 3,000,000 = 0.01 (= 1%)
This is the yield per 90-day period. It is the ‘periodic yield’ for 90 days.

YIELD PICK-UP

If the periodic yield were greater, for example, 1.02% for the same 90-day period, the interest or gain for the 90-day period would be correspondingly greater.

It would become:
3,000,000 x 0.0102 = 30,600.
For the same length of period, a greater periodic yield indicates a better deal, all other things being equal.

WHERE'S THE CATCH

But all other things are hardly ever equal in an efficient market. This is usefully expressed in the phrase ‘There’s no such thing as a free lunch’.
‘No free lunch’ means, if it looks like we’re getting an extra 0.02% for free, we won’t be. We will be paying for it in some way. There will
always be some catch or disadvantage.

Keeping that health warning in mind, let’s continue calculating with yields.

QUOTE UNQUOTE

In wholesale markets, yields are normally expressed as nominal, or quoted, yields (R) per conventional year, rather than periodic yields (r).

Short-term yields are normally quoted on a ‘simple’ basis, per conventional year of 360 or 365 days. To convert between quotes and periodic yields, we simply multiply or divide the rates by an appropriate fraction.

THREE MILLION DOLLARS

Let’s apply this simple multiplication technique to calculate interest for a short-term period, based on a quoted rate for short-term US dollars, which uses a 360-day year.

For example, you deposit $3m for 90 days at a quoted interest rate of 4%, based on a 360-day conventional year. Let's calculate the amount of interest you will enjoy.

DO THE TWO-STEP

We’ll work through this problem in two steps:
(1) Adjust the quoted interest rate to get the periodic yield.
(2) Calculate the interest from the periodic yield.

(1) Periodic yield (r) from quoted rate (R)
r = R x days / year
Where:
R = quoted yield per conventional year = 0.04 (= 4%)
days = number of days in the investment period = 90
year = number of days in a conventional year = 360 for
US dollars here

r = 0.04 x 90 / 360
= 0.01 per 90 days

(2) Interest from periodic yield
Interest = start amount x periodic yield
= $3,000,000 x 0.01
= $30,000

MORE DAYS IN A YEAR

Our calculation of $30,000 of interest for short-term US dollars used a 360-day year. Some other currencies and markets, for example, short-term sterling (£), use a 365-day conventional year.

Let’s apply a 365-day year for £ now.

For example, Your organisation has an opportunity to invest £3m in a Certificate of Deposit (CD). Calculate the redemption value for such a CD which matures in 90 days, quoted in the market at a yield of 4%.

‘Redemption value’ for a CD means the total cash we will receive back at the final maturity, in 90 days’ time.

ONE, TWO, THREE

For this example we need three steps. The first two are the same as before:
(1) Calculate the periodic yield.
(2) Calculate the interest from periodic yield, as before.
(3) Finally, add the interest to the start amount, to calculate the redemption value.

(1) Periodic yield
r = R x days / year
R = quoted yield = 0.04
days = days in investment period = 90
year = days in conventional year = 365 for £ this time

r = 0.04 x 90 / 365
= 0.009863 per 90 days (rounded to the nearest 0.0001%)

(2) Interest
Interest = start amount x periodic yield
= £3,000,000 x 0.009863
= £29,589

(3) Redemption value = end amount
End amount = start amount + interest
= 3,000,000 + 29,589
= £3,029,589

DIFFERENT CONVENTIONS, LESS INTEREST

When we invested £3m at 4% for 90 days, we got back £29,589 of interest. Do you remember when we invested $3m at 4% for the same period, we got a bigger number for our interest, of $30,000?

This difference results from short-term £ using a 365-day conventional year to calculate interest, compared with 360 days for US dollars. These quoting conventions are sometimes known as ACT/365 fixed and ACT/360, respectively. ‘ACT’ refers to the ‘actual’ number of days in the investment period.

BEYOND COMPARE

We’ve seen that returns from fixed-rate short-term investments depend on several factors, including:

  • Headline percentage rates;
  • Quoting conventions;
  • Currency;
  • Amount invested; and
  • Maturity.

Only when all of these variables, and others, are properly quantified and factored in, can we make properly informed comparisons and recommendations.

____________________

Author: Doug Williamson

Source: The Treasurer magazine