6. Note that, this question aims to demonstrate a key application of ordinary annuities in real life-a fully amortized loan 5 Suppose you borrowed $5,000 at an annual interest rate of 6%, compounded annually. If you have to repay it over five years with equal amounts each year. a) What will be the annual repayment? b) Fill up the empty cells in the table below, using annual payment as calculated in a) Compounding period (year) Totals Beginning Baland Annual payment Interest paid Principal paid Ending balance
1 $5000 ____ _____ ______ ______
2 _____ ____ _____ ______ ______
3 _____ ____ _____ ______ ______
4 _____ ____ _____ ______ ______
5 _____ ____ _____ ______ ______
Totals _____ ____ _____ ______ ______
c) Each yearly repayment is divided into two portions. One portion represents the principal paid while the other portion indicates the interest payment. Does the interest payment each year increase or decrease over time? Why does this happen?
d) How much do you owe the bank at the beginning of year 1, year 2, year 3, year 4 and year 5?