Outstanding Loan Balance Calculator - Prospective & Retrospective Methods

Formula

Prospective: OB_k = PMT × a_{n-k}|i; Retrospective: OB_k = P(1+i)^k - PMT×s_k|i

Enter Values

Original Loan Amount ($) *

Original amount borrowed when loan started.

Annual Interest Rate (%) *

Interest rate on the loan (must remain constant for this calculation).

Original Loan Term (years) *

Original loan term when you took out the loan.

Number of Payments Made *

How many monthly payments you've made so far. If 3 years into a 30-year mortgage, enter 36 payments.

Calculation Method *

Prospective method: PV of remaining payments. Retrospective method: FV of original loan minus FV of payments made. Both give identical results for verification.

Results

Interpretation

Outstanding Balance: $283,041.26 | Principal Paid: $16,958.74 | Interest Paid So Far: $53,935.26 | Total Paid: $70,894.00 | Percent of Loan Paid: 5.65% | Current Equity: $16,958.74. After 60 payments (5 years), you've paid only 5.65% of principal but 76% of each payment went to interest initially.

How It Works

Outstanding balance can be calculated two ways: (1) Prospective: present value of all remaining payments, OB_k = PMT × a_{n-k}|i. (2) Retrospective: future value of original loan minus future value of payments made, OB_k = P(1+i)^k - PMT×s_k|i. Both methods must give the same answer, providing a verification check.

Key Points

Use to verify mortgage statement balance for accuracy.
Prospective method: 'How much do I still owe based on future payments?'
Retrospective method: 'Original loan grew, subtract what I've paid.'
Both methods give identical results - use for double-checking.
Useful when considering refinancing - know exact payoff amount.
For home equity calculation: home value - outstanding balance = equity.

References

Broverman, S.A. (2015). Mathematics of Investment and Credit (6th Edition). ACTEX Publications. Chapter 3, Section 3.1.3: Retrospective Form of Outstanding Balance (pages 85-88): OB_k = L(1+i)^k - R×s_k|i. Section 3.1.4: Prospective Form of Outstanding Balance (pages 88-90): OB_k = R×a_{n-k}|i. Example 3.4 (page 89). Both methods yield identical results.

Outstanding Balance Calculator