Question

You are looking to take out a loan. You found two offers available. Option 1: APR of 8.8% compounded quarterly. Option 2: APR of 8.65% compounded monthly Find the APY for each to decide which option is best for your loan. (Do not round until the final answer. Then round to the nearest thousandths as needed.) (a) The APY for Option 1 is %. (b) The APY for Option 2 is % (c) Choose the best offer for your loan: Option 1: 8.8% compounded quarterly Options 2:8.65% compounded monthly

Answer 1

option I: APR of 8.8%.com pounded quarterly, let P=a (Assume) t=1 years. r = 8.8.4. = 0.088 n= 4 (i compounded So by formula for amount quarterly) A = PC! nt ho jnt 4X1 Ed CH 0.088 4 ac 1+ 0.022 224 x (1.02234 Csscanned with Eamscannen x (1.09094682626)

So, Interest Amount - Principal = (1.ogog 4682626) 20 x (o.ogo9468262 Gbe, Inderest A) Hence, So, A = P(it a) Annual Percentage Vield for option 1. is (0. og 094682626).5 = (0.09192 option 2! APR of 8.65% compounded monthly, let, P = d (Assume) t=1 year Y = 8, 6 5 , - 0 0 2 6 5 n=12 ( compounded monthly) nt vnt 0. 0865 12x1 :))2X Ed(4+0.00720833333)/2 = a (1,00720833333)2 =(1,09001311052)2 So, Interest - Amount Amount a Principal, = (1,09001311662)74- x -Co.o9001311652) Hence, b) Annual Percent age field for option 2 is (0.09 001311652)2 = (0.090) =allt 12 A Scanned with Camscanner

'م 1 by comparing APY for option I and APY for option 2, We find that option 2' yields less interest So, option 2 is best best for loan. CSScanned with CamScanner