Question

Problem 1.1 You deposit $1,000 in a bank account earning 5.75% annual compound interest. How much will you have in 3 years?

Problem 1.2 You deposit $1,000 in a bank account earning 5.75% annual compound interest. How many years will it take to double your money?

Problem 1.3 Your bank account is earning 5.75% annual compound interest. How much money do you have to deposit now in order to have $1,000 in 5 years?

Problem 1.4 Bernie Madoff invites you to invest $1,000 in his fund now and be guaranteed at $1,500 in 4 years. What is the effective annual interest rate that Mr. Madoff is promising you?

Problem 1.5 Repeat Problem 1.1 but assume that interest is compounded quarterly at a nominal annual rate of 5.75%.

Problem 1.6 Repeat Problem 1.2 but assume that interest is compounded quarterly at a nominal annual rate of 5.75%.

Problem 1.7 Repeat Problem 1.3 but assume that interest is compounded monthly at a nominal annual rate of 5.75%.

Problem 1.8 You deposit $5,000 in an account earning 5% interest compounded semi-annually for 2 years and 7% interest compounded quarterly thereafter. What is the account value after 7 years?

Problem 1.9 What is the equivalent effective annual (compound) interest rate in Problem 1.8?

Please only solve 1.5 1.6 1.7 1.8 and 1.9 Thank you！

Answer 1

1.5)number of quarters= 3 *4 =12

quarterly rate =5.75/4= 1.4375%

Amount in 3 years =Amount * (1+i)^n

        =1000(1+.014375)^12

       = 1000(1.014375)^12

          = 1000 * 1.186813

           = 1186.81

1.6)Number of quarters= IN [Future value /present value]/IN[+r]

      =IN[2000/1000]/IN [1+.014375]

      =IN[2]/IN[1.014375]

      = .69315/.01427

       = 48.57 quarters or [48.57/4]= 12.14 years approx

1.7)monthly rate = 5.75/12=.47917%

number of months = 5*12 =60

AMount to invest =Future value *(1/(1+i)^n)

           = 1000*(1/(1+.0047917)^60)

         = 1000*(1/(1.0047917)^60)

        = 1000*.75065

         = $ 750.65

1.8)Semiannual rate= 5/2 =2.5%

number of semiannual months = 2*2 =4

Future value at end of year 2 =Amount (1+i)^n

                   = 5000(1+.025)^4

                  =5000 * 1.10381

                 = 5519.06

now ,

quarterly rate = 7/4 = 1.75%

number of quarters in remaining 5 years = 5*4 =20

Account value in 7 years =Future value iin 2 years * (1+i)^n

                  = 5519.06 (1+.0175)^20

                  = 5519.06 (1.0175)^20

                  = 5519.06 * 1.41478

                   = 7808.26