Name: Fre Who is asking: Student Level of the question: All Question: A loan of \$50,000 taken today is payable within five years. a. determine the annual payments within to be made to repay the loan if interest is charged at a rate of 10% compounded annually b. show the amortization schedule Hi Fre, To save some typing let \$A be the amount of the loan, \$P the payment you make each year and i be the annual interest rate. At the end of the first year you owe \$A(1 + i) and you pay \$P so you left owing \$A(1 + i) - \$P Thus at the end of the second year you owe this amount times 1 + i and you pay \$P so you are left owing [\$A(1 + i) - \$P](1 + i) - \$P = \$A(1 + i)2 - \$P[(1 + i ) + 1] This is the amount you owe at the start of the third year so, at the end of the third year you owe this amount times 1 + i and you make a payment of \$P. Likewise in the fourth and fifth years. Thus at the end of the fifth year you owe \$A(1 + i)5 - \$P[(1 + i)4 + (1 + i)3 + (1 + i)2 + (1 + i ) + 1] But, at the end of the fifth year you have paid off the loan so this is zero. Hence \$50,000(1.1)5 - \$P[(1.1)4 + (1.1)3 + (1.1)2 + (1.1 ) + 1] = 0        * Finally (1.1)4 + (1.1)3 + (1.1)2 + (1.1 ) + 1 is the sum of the first five terms of a geometric series so use you knowledge of geometric series to evaluate this sum and then solve equation * for P. Penny