## Exact return of a short-term deposit

##### Published: Feb 2006

Short-term fixed deposits are useful when companies have excess cash to invest for a limited period. For example, a seasonal business with high sales levels at one time of year may have excess cash for a short period before it stocks up for the next big sales period. Other companies may maintain a cash surplus as a contingency for unforeseen events. In either case, the company will want to maximise the return on its surplus cash in the meantime.

Many investors want to calculate the interest that will be earned in order to calculate the exact amount to be received on maturity. Assuming that all of the interest is paid at the end of the period, this can be done using the following formula, which calculates the total return on a short-term deposit:

$$P\:\times\:1\:+\:i\times\frac{n}{y}$$

Where:

• $$P\:=\: principal\: –\: the\: amount\: invested$$
• $$i\:=\: interest \:rate\: –\: which\: is\: quoted\: and\: agreed.$$
• $$n\:= \:number\: of \:days\: to \:repayment$$
• $$y\:= \:number\: of\: days \:in \:year$$

The exact period of the deposit is important if an accurate calculation is to be made. For example, a three month period may be anything from 89 to 93 days – depending on when weekends and bank holidays occur. This includes non-banking days for the country in which the deposit is taken and also the country of the currency being invested. The number of days considered to be in a year also varies according to the currency, as some currencies assume a 360 day year and other currencies a 365 day year.

Let us look at a worked example. Consider a sum of \$100,000 invested at an annual interest rate of 3% for three months (92 days) – on the basis of a 360 day year.

$$The\:total\: return \:will \:be\:=\:100,000\:\times\:1\:+\:0.03\:\times\:\frac{92}{360}\:=\:US\:\:100,756.16$$

##### Conventional calculator

To perform this calculation on a conventional calculator, you need to press the following buttons:

$$\frac{92}{360}\:=\:(this\: gives\: the\: rounded\: result\: 0.2555556)$$

$$\times\:0.03\:= \:(this\: gives \:the\: rounded \:result\: 0.0076667)$$

$$+\:1\:=\: (this\: gives\: the \:rounded\: result\: 1.0076667)$$

$$\times\:100,000\:=\: This\: gives\: the\: rounded \:result\: 100,766.67$$

##### Scientific calculator

Using the scientific calculator on a Windows computer, you need to press the following buttons:

(Start/Programs/Accessories/Calculator/View/Scientific)

$$100000\:*\:1\:+\:0.03\:*\:\frac{92}{360}=$$

This gives the rounded result 100,766.67

##### HP12C

Using an HP12C or equivalent calculator using Reverse Polish Notation:

$$0.3\:ENTER$$

$$92\:\times$$

$$360\:÷$$

$$1\:+$$

$$100,000\:\times$$

This gives the rounded result 100,766.67