HP 10bII+ User Manual page 152

Table 13-12 Calculating the annual percentage rate
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Loan With a Partial (Odd) First Period
TVM calculations apply to financial transactions where each payment period is the same
length. However, situations exist where the first payment period is not the same length as the
remaining periods. This first period is sometimes called an odd or partial first period.
If interest is applied to an odd first period, it is usually calculated as simple interest. So using
the HP 10bII+ to do a payment calculation with an odd first period is a two step process:
1. Calculate the amount of simple interest that accrues during the fractional first period and
add it to the loan amount. This is the new PV. You must be able to calculate the length of
the odd first period as a fraction of the whole period. (For example, a 15-day odd first
period would be 0.5 periods assuming a whole period to be a 30-day month.)
2. Calculate the payment using the new PV, with N equal to the number of full periods. Use
Begin mode if the number of days until the first payment is less than 30; otherwise use
End mode.
Example
A 36-month loan for 4,500 has an annual rate of 15%. If the first monthly payment is made
in 46 days, what is the monthly payment amount assuming 30-day months?
The odd first period in this example is 16 days.
Set to End mode. Press
Table 13-13 Calculating the monthly payment amount
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144 Additional Examples
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if BEGIN annunciator is displayed.
Display Description
12.53 Calculates APR.
Display Description
12.00 Sets payments per year.
15.00 Stores interest rate.
1.25 Calculates periodic interest
rate.
0.67 Multiplies by fraction of a
period.
30.00 Calculates amount of simple
interest owed for odd
period.
4,530.00 Adds this simple interest to
present value.
36.00 Stores term of loan.