Total Cost Reduction Calculator and Loan Savings

Total cost reduction is the difference between the total amount paid under a current loan schedule and the total amount paid under a revised schedule. Enter each schedule’s loan amount, APR, and term to estimate the reduction in total payments, including principal and interest; a positive result means the revised schedule costs less.

Formula

The calculator subtracts revised total payments from current total payments. For each fixed-rate loan schedule, it calculates the monthly payment, rounds that payment to the nearest cent, and multiplies it by the number of monthly payments.

Monthly payment: M = round[P × r / (1 − (1 + r)⁻ⁿ), 2]
Total payments: T = M × n
Total cost reduction: R = T_current − T_revised

• P is the loan principal in dollars.
• r is the monthly interest rate, calculated as APR ÷ 1,200.
• n is the term in months, calculated as years × 12.
• M is the monthly payment in dollars, rounded to cents.
• T is the sum of the rounded scheduled payments in dollars.
• R is the difference in total payments in dollars. Positive means the revised schedule has a lower calculated total; negative means its calculated total is higher.

This comparison measures scheduled payments, not just interest. If principal amounts differ, the totals also reflect that difference. For comparing interest cost alone, subtract the principal from each schedule’s total payments, provided each loan is fully repaid by the modeled payments.

Worked Example

Using the calculator’s defaults, the current schedule has a $20,000 principal, 8% APR, and five-year term. The revised schedule has the same principal and term but a 6% APR.

1. Convert the current APR to a monthly rate: 8 ÷ 1,200 = 0.0066667. The term is 5 × 12 = 60 months.
2. Calculate its payment: $20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰] = about $405.53 after rounding.
3. Calculate current total payments: $405.53 × 60 = $24,331.80.
4. For the revised schedule, the monthly rate is 6 ÷ 1,200 = 0.005, over 60 months. Its payment is $20,000 × 0.005 ÷ [1 − (1.005)⁻⁶⁰] = $386.66 after rounding.
5. Calculate revised total payments: $386.66 × 60 = $23,199.60.
6. Subtract: $24,331.80 − $23,199.60 = $1,132.20 total cost reduction.

Assumptions

• Each schedule has a fixed APR and equal monthly payments.
• Payments are modeled monthly; the first payment follows the usual amortizing-loan timing, one month after the balance is advanced.
• Interest is calculated monthly at APR ÷ 12, with no separate daily-interest adjustment.
• Payments are rounded to cents, and total payments use that rounded amount multiplied by the number of months.
• Fees, taxes, insurance, PMI, escrow, and any final payment adjustment are not included.

What Total Cost Reduction Means

The phrase can describe savings from changing a loan, paying it off sooner, lowering its rate, or reducing the amount borrowed. The comparison is only meaningful when the two totals cover comparable obligations and the same kinds of costs. This calculator compares two standard, fully amortizing payment schedules from the inputs; it does not determine whether a real transaction has extra charges or different payment rules.

A lower monthly payment does not automatically mean a lower total cost. For example, a longer term can reduce the scheduled payment while adding more monthly payments. Conversely, a shorter term may raise each payment while reducing the total paid. Compare both the total and the payment amount, and account separately for transaction costs or changes to the loan balance.

How to Use the Comparison

• Enter the current principal, APR, and term as they apply to the schedule being compared.
• Enter the revised principal, APR, and term. Use the amount actually financed, not an assumed amount, if costs are added to the balance.
• Read the reduction first, then check both displayed totals. A negative result means the revised schedule costs more in this model.
• For a real comparison, obtain the relevant APR, financed amount, term, payment frequency, and fees from the lender’s disclosures. Enter any fee financed into the revised principal; separately paid fees are not included here.

When comparing a refinance or replacement loan, the old loan’s remaining balance and remaining term are usually more relevant than its original amount and term. Compare the remaining payments on the existing loan against all payments on the proposed replacement, and include any costs that apply to the change. The calculator cannot infer these figures or decide which costs belong in a particular comparison.

Limits and Common Misreadings

The result is a straightforward cash-payment comparison, not a present-value calculation. It treats a dollar paid today and a dollar paid years from now equally, and it does not model inflation, investment returns, variable rates, skipped payments, extra principal payments, or changing fees. Its standard formula also assumes each schedule is fully amortizing with equal monthly payments.

Rounding matters: the calculator rounds each monthly payment to cents before multiplying by the term, so its total may differ slightly from a calculation that keeps fractions of a cent throughout. Actual contracts may adjust the final installment to clear a small remaining balance. Entering an APR or term incorrectly can have a much larger effect than rounding.

A common misconception is that “cost reduction” always means interest savings. Here it means the difference in total scheduled payments, which includes repayment of principal. If the revised principal differs, the result is not an apples-to-apples measure of interest savings. For interest-only comparison, calculate each schedule’s interest as total payments minus principal, then compare those figures; fees still need separate treatment.

Frequently Asked Questions

Is total cost reduction the same as interest savings?
No. This calculator subtracts total scheduled payments, including principal. Interest savings compare the interest portions only and should account for any changes in principal and separately paid costs.

Can a lower monthly payment increase the total cost?
Yes. A longer repayment term can lower the monthly amount but require more payments overall. Check the total payments as well as the monthly payment.

Should fees be included in the comparison?
Fees are not included automatically. If a fee is added to the new loan balance, include it in the revised principal. Costs paid separately should be added to the comparison outside this calculator.

What does a negative reduction mean?
It means the revised schedule’s calculated total payments exceed the current schedule’s total payments, based on the values entered and the calculator’s assumptions.

Does this calculator cover variable-rate loans or extra payments?
No. It assumes a fixed APR and equal monthly payments, with no extra payments. Those situations require a schedule that models rate changes or additional principal payments.

This result is an estimate, and the lender’s disclosure gives the exact figures.

Related

• Initial Escrow Account Calculator: Estimate Closing Funds
• Mortgage Refinance Costs: Fees and Break-Even
• Home Refinance Cost: Fees, Examples, and What to Expect

in oldp | Current loan amount | $ | 20000 | 1 | 100000000
in oldr | Current interest rate (APR) | % | 8 | 0.01 | 100
in oldy | Current loan term | years | 5 | 0.0833 | 50
in newp | Revised loan amount | $ | 20000 | 1 | 100000000
in newr | Revised interest rate (APR) | % | 6 | 0.01 | 100
in newy | Revised loan term | years | 5 | 0.0833 | 50
out red | Total cost reduction | $ | (round(oldp * (oldr / 1200) / (1 - (1 + oldr / 1200) ^ -(oldy * 12)), 2) * oldy * 12 + 0 * sqrt(oldy) - (round(newp * (newr / 1200) / (1 - (1 + newr / 1200) ^ -(newy * 12)), 2) * newy * 12 + 0 * sqrt(newy)) | 2
out oldtot | Current total payments | $ | round(oldp * (oldr / 1200) / (1 - (1 + oldr / 1200) ^ -(oldy * 12)), 2) * oldy * 12 | 2
out newtot | Revised total payments | $ | round(newp * (newr / 1200) / (1 - (1 + newr / 1200) ^ -(newy * 12)), 2) * newy * 12 | 2