For an amortization schedule, calculates the principal amount paid over a range of payments.

ΣPrn(*paymentt1*, *payment2*, [*roundvalue*])

On the TI-83, press:

- 2nd FINANCE to access the finance menu.
- 0 to select ΣPrn(, or use arrows and ENTER.

On the TI-83+ or higher, press:

- APPS to access the applications menu.
- 1 or ENTER to select Finance…
- 0 to select ΣPrn(, or use arrows and ENTER.

TI-83/84/+/SE

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The `ΣPrn(` command calculates, for an amortization schedule, the principal amount over a range of payments: the portion of those payments that went toward paying off the principal. Its two required arguments are *payment1* and *payment2*, which define the range of payments we're interested in. However, it also uses the values of the finance variables PV, PMT, and I% in its calculations.

The optional argument, *roundvalue*, is the number of digits to which the calculator will round all internal calculations. Since this rounding affects further steps, this isn't the same as using `round(` to round the result of `ΣPrn(` to the same number of digits.

Usually, you will know the values of ` N`,

`PV`, and

`I%`, but not

`PMT`. This means you'll have to use the finance solver to solve for

`PMT`before calculating

`ΣPrn(`; virtually always,

`FV`will equal 0.

# Sample Problem

*Imagine that you have taken out a 30-year fixed-rate mortgage. The loan amount is $100000, and the annual interest rate (APR) is 8%. Payments will be made monthly. How much of the principal amount was paid in the first five years?*

We know the values of ` N`,

`I%`, and

`PV`, though we still need to convert them to monthly values (since payments are made monthly).

`is 30*12, and`

**N**`I%`is 8/12.

`PV`is just 100000.

Now, we use the finance solver to solve for `PMT`. Since you intend to pay out the entire loan, `FV` is 0. Using either the interactive TVM solver, or the `tvm_Pmt` command, we get a value of about -$733.76 for `PMT`.

We are ready to use `ΣPrn(`. We are interested in the payments made during the first five years; that is, between the 1^{st} payment and the 5*12=60^{th} payment. `ΣPrn(1,60)` gives us the answer: -$4930.14 (the negative sign simply indicates the direction of cash flow)

# Formulas

The formula that the calculator uses for `ΣPrn(` is in terms of `bal(`:

When the *roundvalue* argument isn't given, we can substitute the explicit formula for `bal(` and simplify to get the following formula:

# Error Conditions

**ERR:DOMAIN**is thrown if either payment number is negative or a decimal.

# Related Commands

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