HP12c+ Financial Calculator Emulator

If the selector in the lower-right corner of the display area or the L key is activated, the values of the financial variables n, i, PV, PMT, FV, %GV and AV can be displayed above their corresponding keys for greater convenience.

Calculation of variable annuities in geometric and arithmetic progression has been implemented, together with the constant annuities supported by the HP12c. When %GV = 0 and AV = 0, TVM12c+ treats the cash flow as a constant annuity.

General operation is the same: enter the values of the known variables and press the desired variable so that the calculator computes its value. The cash-flow sign convention must also be observed.

If %GV ≠ 0 and AV = 0, calculations are performed for a variable annuity in geometric progression, with growth rate %GV, applied over the periods specified by n and taking the remaining financial variables into account. The value of PMT corresponds to the first term of the annuity. If \(q=\%GV/100\), \(i=i\%/100\), and \(\mu\) is defined as an indicator of the payment timing, the financial equation used is:

\[ 0 = PV + PMT\,(1+i\mu)\, \frac{1-\left(\displaystyle\frac{1+q}{1+i}\right)^n}{i-q} + \displaystyle\frac{FV}{(1+i)^n} \]

The parameter \(\mu\) makes it possible to handle both ordinary annuities and annuities due within the same expression. If \(\mu=0\), the annuity is ordinary (END) and \((1+i\mu)=1\), so this factor does not change the result. If \(\mu=1\), the annuity is due (BEGIN) and the factor becomes \((1+i)\) shifting every payment one period toward the present.

For the special case \(i=q\), the geometric-annuity factor is replaced by \[ (1+i\mu)\,\frac{n}{1+i} \]

Example. Given a variable annuity in geometric progression with a first payment of $10\:000$, increasing by $20\%$ annually, a duration of $15$ years, and an effective interest rate of $6\%$, determine its present value and future value.

After clearing the financial registers, in ordinary-annuity mode (END, \(\mu=0\)) and observing the cash-flow sign convention, enter 10000 H PMT, 20 %GV, 15 n and 6 i. The result is:

\[ PV = 387.772,27 \] \[ FV = 929.318,81 \]

If %GV = 0 and AV ≠ 0, calculations are performed for a variable annuity in arithmetic progression, with increment AV, a first payment equal to PMT, and n periods. Under the cash-flow sign convention, for example, if PMT = -500 and the amount increases by 25 each period, enter AV = -25. Defining \(i=i\%/100\), \(v=(1+i)^{-1}\), \(a_{\overline{n}|i}=\dfrac{1-v^n}{i}\), and \(\mu\) as an indicator of the payment timing, the financial equation used is:

\[ 0 = PV + (1+i\mu)\left[ PMT\,a_{\overline{n}|i} + AV\,\displaystyle\frac{a_{\overline{n}|i}-n v^n}{i} \right] + FV\,v^n \]

The parameter \(\mu\) makes it possible to handle both ordinary annuities and annuities due within the same expression. If \(\mu=0\), the annuity is ordinary (END) and \(1+i\mu=1\), so this factor does not change the result. If \(\mu=1\), the annuity is due (BEGIN) and the factor becomes \(1+i\), shifting every payment one period toward the present.

Example. Determine the present value of an annual variable annuity in arithmetic progression, with a first payment of $10\:000$, increasing by $2\:000$ annually, a duration of $20$ years, and an interest rate of $5\%$.

After clearing the financial registers, in ordinary-annuity mode (END, \(\mu=0\)) and observing the cash-flow sign convention, enter 10000 H PMT, 2000 H AV, 20 n and 5 i. Pressing PV gives:

\[ PV = 321.598,93 \]

If %GV ≠ 0 and AV ≠ 0, the calculator displays Error 5.

An HP12c calculator quick reference guide is available in PDF format.