1. Please simplify your answers as far as possible without a calculator. You may leave your answers in terms of exponential and logarithmic expressions. (a) John invests $5,000 in an account with semi-annual compounding and an annual interest rate of 4%. How much money will he have after 35 years? Answer with units: A=p(1+rt)->simple B= p(1+r/m)*mt->compound $5000(1.02)^70 C=pe^rt-->continous P=5000 m=2 1=.04 1=35 A=5000(1+.04/2)^2*35 =5000(1.02)*70 (b) $7000 was deposited in a bank account earning 5.5% interest compounded continuously. How long will it take for the amount in the account to double? Answer with units: 5000(1.02)*70 years CC=pe^r p 7000 1 .055 t=? Ine=1 ALWAYS 2(7000)=7000*e^_055't divide both by 7000 2-e^.055t Ln2-Lne^.0551 In2=,055t Ine t=In2/.055 (c) Assume that the yearly rate of price inflation for housing in the the next ten years is 3.5% and assume that this is compounded annually. A house costing $780,000 today will cost more in ten years. How much will it cost in ten years? Answer with units