Find the payment necessary to amortize the loan using the amortization table. Round to the nearest cent.
-The Meyers bought a Sandwich City franchise for $500,000. They paid $100,000 of their own money and borrowed the rest, agreeing to make semiannual payments over 8 years at 8% (compounded semiannually).

Question

Find the payment necessary to amortize the loan using the amortization table. Round to the nearest cent.  
-The Meyers bought a Sandwich City franchise for $500,000. They paid $100,000 of their own money and borrowed the rest, agreeing to make semiannual payments over 8 years at 8% (compounded semiannually).

Quizplus · Accepted Answer

The correct answer is found by calculating the semiannual payment on an amortizing loan using the formula for the payment on an annuity: P = [rPV] / [1 - (1 + r)^-n], where P is the payment, r is the interest rate per period, PV is the present value of the loan, and n is the total number of payments. Here, PV = $400,000 (the amount borrowed), r = 0.04 (8% annual interest compounded semiannually gives a per period rate of 4%), and n = 16 (8 years of semiannual payments). Plugging these values into the formula gives the semiannual payment amount, which matches choice A.

Find the Payment Necessary to Amortize the Loan Using the Amortization