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 Payment | Annual APR | Term (Months) | Original Principal (-PV) | Total Interest Paid |
|---|---|---|---|---|
| $650.00 | 6.00% (0.50%/mo) | 60 | $33,621.61 | $5,378.39 |
| $650.00 | 0.00% (Promo) | 60 | $39,000.00 | $0.00 |
| $650.00 | 7.20% (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.