# HP 10BII Instruction Manual page 2

Simple and compound interest
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HP 10BII Simple and Compound Interest
The time value of money application
The time value of money application built into the HP 10BII is used to solve compound interest problems and annuities
that involve regular, uniform payments. Compound interest problems require the input of 3 of these 4 values:
ABCE. Annuity problems require the input of 4 of these 5 values: ABCDE. Once these
values have been entered in any order, the unknown value can be computed by pressing the key for the unknown value.
The time value of money application operates on the convention that money invested is considered positive and money
withdrawn is considered negative. In a compound interest problem, for example, if a positive value is input for the C,
then a computed Ewill be displayed as a negative number. In an annuity problem, of the three monetary variables, at
least one must be of a different sign than the other two. For example, if the Cand Dare positive, then the Ewill
be negative. If the Cand Eare both negative, then the Dmust be positive. An analysis of the monetary situation
should indicate which values are being invested and which values are being withdrawn. This will determine which are
entered as positive values and which are entered as negative values.
Interest rates are always entered as the number is written in front of the percent sign, i.e., 5% is entered as a 5 rather
than as 0.05.
Simple and compound interest
Simple interest is generally used for short duration deposit or loan arrangements. It is often used for accounts holding
cash balances that change each day. Many car loans are arranged using simple interest. Interest is computed for the
entire time period under consideration only at the end of the period. On a car loan, the interest would be computed from
the last date a payment was made until the next date a payment is made. The basic relationship is given by the formula
shown in figure 1 below.
In this formula, I is the interest, P is the principal, R is the simple interest rate and T is the time expressed in years or
portions of a year. If the time is measured in months, then T would be the fraction of the number of months under
consideration divided by 12. If the time is measured in days, T will be a fraction of the number of days under
consideration divided by 365 if using exact interest or divided by 360 if using ordinary interest.
The ending amount is therefore equal to the principal plus the interest. This is illustrated by the formula in figure 2 below.
In this formula, FV is the future or ending value, I is the interest and P is the principal.
Compound interest periodically computes the interest accrued or earned and adds it to the value of the account or to the
amount owed on a loan. The period for which is compounding occurs can vary from daily to annually. For the same
amount of time, a compound interest deposit will grow to be much larger than the same size deposit in a simple interest
account. This is because interest earned will be computed each period and added to the balance of the account. During
the next period, the interest earned the previous period will then earn interest. It is this interest-earning-interest that gives
compound interest the remarkable ability to turn a small deposit into a very large deposit over time. The basic
relationship is given by the formula shown in figure 3 below.
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I = PRT
FV = P + I
FV = PV × 1+ i
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Figure 1
Figure 2
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Figure 3
HP 10BII Simple and Compound Interest - Version 1.0