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Financial & Accounting

Calculate Original Loan Amount & Borrowing Limit from Monthly Payment (PV)

Back-solve the original loan principal or maximum affordable loan balance from a fixed periodic payment, annual interest rate, and term in months using PV.

Reverse-engineer initial principal when you know the payment, APR, and term

Equipment leases and affordability calculators often start from a target monthly payment (for example, $650/month for 60 months at 6.00% APR) and ask how much principal that payment amortizes.

Passing periodic rate APR / 12, total months nper, and negative cash outflow -payment (or negating -PV(APR / 12, months, payment)) computes the exact initial principal, including the 0% promotional-rate case where PV cleanly returns payment * months.

Monthly PaymentAnnual APRTerm (Months)Original Principal (-PV)Total Interest Paid
$650.006.00% (0.50%/mo)60$33,621.61$5,378.39
$650.000.00% (Promo)60$39,000.00$0.00
$650.007.20% (0.60%/mo)48$27,039.23$4,160.77

Original Loan Principal Back-Solved via PV

Validates payment B2 > 0, APR B3 >= 0, and months B4 >= 1, returning the positive initial principal.

=IF(OR(B2 <= 0, B3 < 0, B4 < 1), "Invalid Loan Inputs", ROUND(-PV(B3 / 12, B4, B2), 2))

Implied Total Interest Over Full Amortization Term

Subtracts the recovered original principal from total scheduled payments B2 * B4.

=ROUND(B2 * B4 - (-PV(B3 / 12, B4, B2)), 2)

Try the example

Use the original values or change them to test your understanding.

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