# Simple and Compound Interest

## The time value of money application

The time value of money application built into the HP 17bII+ is used to solve compound interest problems and annuities that involve regular, uniform payments. This application is accessed from the main menu level of the HP 17bII+ by pressing
then
.

If you do not see
displayed on the screen, you may be inside a different menu. You can return to the main menu and select the
menu by pressing
.

When you enter the TVM environment for the first time, the screen will appear as shown in Figure 1 below.

Compound interest problems require the input of 3 of these 4 values:
. Annuity problems require the input of 4 of these 5 values:
. Once these values have been entered in any order, the unknown value can be computed by pressing the key for the unknown value.

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. Values for N are always the total number of periods – if a problem has an interest rate that is compounded monthly and the time frame is 5 years, the value entered for N would be 60 total periods.

## 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 2 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 3 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 4 below.

In this formula, FV stands for the future value, PV is the present value, I is the interest rate per period, and N is the total number of periods. The interest rate per period is computed by taking the nominal annual rate and dividing by the number of periods per year.

Compound interest problems can be directly solved using the time value of money application. The nominal annual
interest rate is entered and the HP 17bII+ automatically uses the value for the number of periods per year to compute the
interest rate per period. Simple interest problems are solved as basic arithmetic problems.

## Practice solving time value of money problems

### Example 1

If you deposit $175 today, how much is it worth in 10 years, if interest is compounded at a 4% annual rate?

### Answer

The answer is $-259.04.

NOTE:The solution is displayed as a negative value. The problem is set up with the $175 as a deposit. The value at the end of the 10-year period would be a withdrawal and is therefore shown as a negative value.

### Example 2

If you owe $500 today, how much do you owe in 3 months, if the debt accumulates interest at 5% simple interest?

### Solution

In Algebraic mode, press the following:

In 'RPN' mode, press the following:

### Answer

The answer is $506.25.

### Example 3

If you deposit $1,234 today, how much do you have in the account in 87 days, if the deposit earns interest at 4% simple interest, using ordinary interest?

### Solution

Since the deposit will earn interest using ordinary interest, the T fraction will have 360 as the denominator.

In Algebraic mode, press the following:

In 'RPN' mode, press the following:

### Answer

The answer is $1,245.93.

### Example 4

If you want $1,000,000 when you retire in 40 years, how much must you deposit today into an account earning interest at 7%, compounded monthly?

### Answer

The answer is $61,306.77. The $1,000,000 amount is entered as a negative number since it will be a withdrawal from the account in 40 years.

### Example 5

What interest rate, compounded semiannually will cause an initial deposit of $400 to grow to become $600 in 5 years?

### Answer

8.28%, compounded semiannually.

### Example 6

How long would it take before an initial deposit of $2,345 would grow to become $3,456, if the account earns interest at 5%, compounded monthly?

### Answer

93.27 months or approximately 7.8 years. In actuality, the balance in the account would not exceed $3,456 until month 94.

### HP Support forums

Find solutions and collaborate with others on the HP Support Forum