HP 12C Learn
Loan APR from PMT
Solve for the interest rate when payment, loan amount, and term are already known.
7 min| Draft
What this solves
This tutorial helps users back out the implied loan rate when the payment amount is already known.
Before you start
- Clear the financial registers first.
- Confirm whether the payment is monthly, quarterly, or annual.
- Use opposite signs for PV and PMT.
Key ideas
The returned i is periodic
If n is monthly, the solved i is monthly until you convert it.
Worked example 1
Example: estimate the monthly rate from payment
You know the loan amount, monthly payment, and loan term. You want the implied periodic rate.
Setup
- Use END mode.
- Treat the payment and loan amount as opposite-direction cash flows.
Inputs
- Loan amount (PV)
- 250,000
- Monthly payment (PMT)
- 1,498.88
- Term (n)
- 360 months
- Future value (FV)
- 0
Keystrokes and checkpoints
1
f CLEAR REG
Reset the TVM state.
Display: 0
2
360 n
Store the number of periods.
Display: 360
3
250000 PV
Enter the present value.
Display: 250000
4
1498.88 CHS PMT
Enter the recurring payment with the opposite sign.
Display: -1498.88
5
0 FV
Set the terminal balance to zero.
Display: 0
6
i
Solve for the periodic rate.
Display: Monthly rate
Result
The display shows the monthly rate implied by the loan assumptions.
Interpretation
That result is periodic, not automatically an annual APR.
Sanity checks
- If the result seems impossible, clear the registers and re-enter only the required values.
- If you expected an annual figure, you are likely misreading a monthly result.
Why it works
- The HP 12C solves the missing variable once the other TVM variables are consistent.
- The meaning of i depends on the unit used by n.
- APR interpretation fails when the period conversion step is skipped.
Common mistakes
- Treating the returned monthly rate as an annual APR.
- Using the same sign for PV and PMT.
- Solving for i without resetting old TVM values first.
Practice prompt
After solving the monthly rate, convert it to an annual figure using the convention your use case expects.
Try it in the HP 12C emulator
Follow the steps above, then test the sequence live.