Please answer all questions and show work for every question. Provide detailed explanations, step by step break downs for explanation, written explanations, etc. Please Write neatly, circle final answers, and circle final written explanations, I definitely will leave a great rating! Please write on paper and don't respond if you already have answered.

For the following problems, write the equation that is relevant to solve the problem, the values of the variables that you will use in that equation, and a complete sentence stating what your answer to the question is. Your answer must include appropriate units 1. Five and a half years ago, Elena invested $20,000 in a retirement fund that grew at a rate of 2.96% compounded continuously. What is the investment worth today? What was the interest earned for that investment so far? 2. How long will it take for an investment with an annual rate of 2.85% compounded quarterly to double in value? (Doubling time). How long will it take for the same investment to quadruple in value? 3. Bank A offers a loan with an annual interest rate of 42% compounded quarterly. Bank B offers a loan with an annual interest rate of 4.18% compounded continuously. Use the APY to determine which bank offers a better deal. 4. American Express's online banking division offers a money market account with an APY of 2.243%. If interest is compounded monthly, what is the equivalent annual interest rate? 5. The parents of a young child want to establish a sinking fund for her college education. If they estimate that they will need $150,000 in 12 years, how much should they pay monthly at 2.3% to reach that amount? How much interest will this investment generate? (1) The formula for continous compounding is given by : A = Pxet We have given : P= $20, 000 r= 2. 96% or 0.0296 t = 5-5 years put in equation ( i): A = py ert A= 20 000 x 0.0296x5-5 A = 20,000 X 8 0.16280 A= 23536-026117 A4 23 536 . 03 Now interest rate earned is given by : Interest earned = total amount - Principle amount = 235 36.03- 20,530 = 3536. 03 So , interest earned for that truestment so for approximately is $35 36 . 03 CS Scanned with CamScanner4 p = P ( 1 + 0 . 0285) 45 4 4 = 1 1+ 0.0285 4 4 t 4: ( 1+ 0.007125 ) 4 = ( 1. 00 7125 ) (1. 00 7125 ) 45 = 4 Take log on both: In ( 1 .00 7125 ) "t = en ( 4 ) 4+ en ( 1. 007125 ) = en ( 4 ) Divide both way 4 en ( 1 . 007/ 25 ) wt In ( 1.067/25 ) en ( y ) Men ( 1-007125) - yen ( 1.007125 ) t. = 48. 8/ 4989 years (3, Offer from Bank A Rate of Interest = = 4.2 % = 0.042 compounded quarterly = n = 4 Rate of Interest = r= 0.042 0. 0105 ARY = ( 1+ * ) " - 1 ARY = ( 1+ 0: 0 42 ) " - 1 CS Scanned with CamScanner(2 ) Given data : Interest rate (r ) = 2. 85 ! _ - No. of terms (n) = 4 :. ( compounded quarterly ) ( a ) Doubling time is calculated as : Divide the To fromannual Doubling time = 7%% . . intrest vaTe ( 21-85) = 70 r= 2-85 2-85 = 24.56 So doubling time is 24 .56 years (b ) Interest rate =re 2.85 2 or r= 0 . 0 285 compounded quartally = n = 4 let: P Investment be 4P ( : quadruple ) amount in t years Put all in compound interest formula: A = P ( 1 + r )nt Put r= 0.0285, n=4 A = 4P CS Scanned with CamScanner(n ) To calculate the equivalent amual interest vale , we need to consider the effect of compounding . With monthly compounded , we can use forla: leg = ( 1 + 1 ) " - 1 = (1+ 0.02243 ) 12 IL : Y = 0.0 2243 7 = 12 = (1. 0 0 / 86 9 16 667 ) - 1 = 2. 26 62 % Therefore , the equivalent annual interest rate , 'when Interest is compounded monthly is approximately 2.2662 ? CS Scanned with CamScannerADY = ( 1+ 0.042) 9 - 1 4 APY = 1. 04267 - 1 ADY = 0. 04267 Apy = 4.267 % offer from Bank B rate of Interest = 4.18% = 0.0418 continusoly compounded = n= 1 APY = ( 1 + 5 ) Apy = (1+ 0.0418) - 1 APY = ( 1+ 0.0418 ) - 1 APy = 1 + 0.0 418 - 1 APy = 0.0 418 ADY = 4.18 %% Bank A offers loan at an effective rate of 4.267 % Bank B offers loan at an effective rate of 4.18% Bank B offers a better deal as it has lower interest rate as compounded to Bank A. CS Scanned with CamScanner