Months saved, interest saved, new end date

Assumptions

• The rate is a nominal annual rate, divided by 12. It is not an APR. An Irish APR includes fees and is a different number.
• Interest is charged monthly on the balance at the start of the month and rounded to the cent, half up.
• The regular payment is the standard annuity payment, rounded to the cent. A cent or two left on the original end date is cleared in that last payment.
• The lump sum comes off the balance on the start date, before the first interest charge. Monthly overpayments are added on top of the contractual payment and reduce the principal.
• The rate does not change. Break fees, mortgage insurance, tax relief, and a switch to a lower repayment (instead of a shorter term) are not modelled.
• The start date is the first contractual payment. The end date is the date of the last payment.

How this is calculated

• Payment = P × r × (1 + r)^n / ((1 + r)^n − 1), where r is the monthly rate and n is the number of months left. At 0% the payment is the balance divided by the months.
• A standard check: €100,000 at 6% for 30 years is €599.55 a month.
• Interest saved is the interest on the original schedule minus the interest on the new one, both rounded the same way.