Question

Two accounts earn simple interest. The balance y (in dollars) of Account A after x years can be modeled by y=10x 500. Account B starts with $400 and earns 5% simple annual interest.

Question I need help with: Which account has a greater principal, and how much greater is the principal? Which account has a greater annual interest rate, and how much greater is the annual interest weight?

Answer 1

In an installment loan, a lender loans a borrower a principal amount P, on which the borrower will pay a yearly interest rate of i (as a fraction, e.g. a rate of 6% would correspond to i=0.06) for n years. The borrower pays a fixed amount M to the lender q times per year. At the end of the n years, the last payment by the borrower pays off the loan.

After k payments, the amount A still owed is

A = P(1+[i/q])k - Mq([1+(i/q)]k-1)/i, = (P-Mq/i)(1+[i/q])k + Mq/i. The amount of the fixed payment is determined byM = Pi/[q(1-[1+(i/q)]-nq)]. The amount of principal that can be paid off in n years isP = M(1-[1+(i/q)]-nq)q/i. The number of years needed to pay off the loan isn = -log(1-[Pi/(Mq)])/(q log[1+(i/q)]). The total amount paid by the borrower is Mnq, and the total amount of interest paid isI = Mnq - P.