Final answer:
The formula after solving for P is the present value of an annuity formula, used to calculate the amount of a loan based on payment, rate, and number of payments. Making 13 monthly payments per year on a loan instead of 12 can reduce both the loan term and the total interest paid.
Step-by-step explanation:
The question you've asked pertains to solving the monthly payment formula for the principal amount P. If you solve for P in the formula M = pr(1 + r)^n / ((1 + r)^n - 1), you get the present value of an annuity formula. This is a widely-used formula in finance to determine the amount of a loan based on regular payments, interest rate, and the number of payments.
For example, if you take a $300,000 loan at a 6% annual interest rate, convertible monthly, and make monthly payments over 30 years, you would use this formula to calculate your monthly payments. If you make larger monthly payments by a fraction of 12, effectively making 13 payments a year, you would save time and money because more of your payment is going towards the principal earlier in the loan term, thereby reducing the amount of interest that accrues over the life of the loan.