Time value of money calculator, with BA II Plus steps

Solve for any one of N, I/Y, PV, PMT and FV. You get the answer, the working and the keys to press on a BA II Plus.

Present value

7,721.73

Positive: money you receive.

The working

Equation of value at time 0, with money out negative: $PV$ ${}+ PMT\,a_{\overline{10}|}$ ${}+ FV\,v^{10}$ $= 0$ .
At $i$ $= 0.05$ : $a_{\overline{10}|}$ $= \dfrac{1 - v^{10}}{i}$ $= 7.72173$ and $v^{10}$ $= 0.613913$ .
$PV = -\left(-1{,}000.00 \times 7.72173 + 0.00 \times 0.613913\right) = 7{,}721.73$ .

On a BA II Plus

Clear the five keys2ndCLR TVM
One payment a period2ndP/Y1ENTER2ndQUIT
Payments at the endNothing to press unless the screen shows BGN. If it does:2ndBGN2ndSET2ndQUIT
Number of periods10N
Interest rate per period (%)5I/Y
Payment each period1000+|−PMT
Future value0FV
ComputeCPTPV

Enter money paid out as a negative number with the +|− key. I/Y is the rate per period, as a percent.

Amortization schedule

Payment	Amount	Interest	Principal	Balance
1	1,000.00	386.09	613.91	7,107.82
2	1,000.00	355.39	644.61	6,463.21
3	1,000.00	323.16	676.84	5,786.37
4	1,000.00	289.32	710.68	5,075.69
5	1,000.00	253.78	746.22	4,329.48
6	1,000.00	216.47	783.53	3,545.95
7	1,000.00	177.30	822.70	2,723.25
8	1,000.00	136.16	863.84	1,859.41
9	1,000.00	92.97	907.03	952.38
10	1,000.00	47.62	952.38	0.00

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What the five keys mean

N	The number of payment periods
I/Y	The interest rate per period, as a percent
PV	The value at the start: a loan received is positive, a deposit made is negative
PMT	The level payment each period
FV	The value at the end of the last period

Signs: money out is negative

The calculator balances one equation: PV, plus the payments, plus FV, all valued today, add to zero. So money you pay out and money you receive must have opposite signs.

Borrow 20,000 and the PV is positive; the repayments are negative. Deposit 1,000 a year and PMT is negative; the balance you take out at the end, FV, is positive.

Try it on an exam question

Question 1

A winner will receive $5,000 at the end of each year for 10 years from a lottery. The annual effective interest rate is 6.0%.

Calculate the present value of the payments.

Question 2

Ada borrows $20,000, repaid by level payments at the end of each year for 5 years at an annual effective interest rate of 6.0%.

Calculate the level payment.

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Questions people ask

How do you solve time value of money on a BA II Plus?

Clear the row with 2nd then CLR TVM, set P/Y to 1, type each known value followed by its key (N, I/Y, PV, PMT or FV), then press CPT and the key you want. Enter money paid out as a negative number.

Why does the BA II Plus show Error 5?

Error 5 means no answer exists for the values entered. The usual cause is that every amount has the same sign: money paid out must be negative and money received positive.

What should P/Y be on a BA II Plus?

Set P/Y to 1 and enter the interest rate per period as I/Y. Then N is the number of payments, whether they are monthly, quarterly or yearly. A reset BA II Plus has P/Y at 12, and a BA II Plus Professional has it at 1.

What is the difference between END and BGN?

END treats payments as made at the end of each period, an annuity-immediate. BGN treats them as made at the beginning, an annuity-due, which is worth one period's interest more.

Is the BA II Plus allowed on Exam FM?

Yes. The BA II Plus and the BA II Plus Professional are both on the Society of Actuaries' list of approved calculators.