HP 12C Learn

Loan APR from PMT

Solve for the interest rate when payment, loan amount, and term are already known.

7 min

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.
  • This simple example assumes no loan fees; fees can change the APR.

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: 0.00
2
g END
Select end-of-period payments. The BEGIN indicator should be off.
3
360 n
Store the number of periods.
Display: 360.00
4
250000 PV
Enter the present value.
Display: 250,000.00
5
1498.88 CHS PMT
Enter the recurring payment with the opposite sign.
Display: -1,498.88
6
0 FV
Set the terminal balance to zero.
Display: 0.00
7
i
Solve for the periodic rate.
Display: 0.50

Result

The implied rate is about 0.50% per month.

Interpretation

With no loan fees, multiplying the unrounded monthly rate by 12 gives about 6.00% nominal annual interest; this is not the effective annual rate. The payment was rounded to cents, so the recovered rate is approximate. If fees reduce the amount actually received, use that net amount as PV to estimate the APR paid.

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.

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