Installment Loan Calculator
If Kendall switched payments from yearly to monthly, how long would it take to pay the loan off?
Kendall borrows $100,000 on January 1, 1993 to be repaid in 12
annual installments at an effective annual rate of interest of 8%. The first payment is due on January 1, 1994. Instead of annual payments she decides to make monthly payments equal to one twelfth the annual payment beginning on February 1, 1993. Determine how many months will be needed to pay off the loan only using pencil, paper, and TI BAII Plus financial calculator.
Please show the steps.
This is a study question for an actuarial exam, which have pretty arbitrary questions. This is unreasonable in real life, but the question exists to teach actuarial concepts.
You couldn’t arbitrarily decide to make the monthly payments as one twelfth of the annual payments, math doesn’t work that way and I don’t have a TI BAll Plus financial calculator.
Effectively what must happen is that the payments go from annual to monthly, and instead of paying $14,902.95 annually for ten years, Kendall will be making 120 payments of $1213.28. Those latter payments total $14,559.31 for a year. The reason they total less than $14,902.95 is because the principal is being reduced each month instead of annually.
