Question

You have an investment account that started with ​$1 comma 0001,000 1010 years ago and which now has grown to ​$6 comma 0006,000. a. What annual rate of return have you earned​ (you have made no additional contributions to the​ account)? b. If the investment account earns 16 %16% per year from now​ on, what will the​ account's value be 1010 years from​ now?

Answer 1

1) Calculation of annual rate of return :

             Annual rate of return = (pricipal + interest / pricipal)^1/10 -1

                                            = (6000/1000)^{0.1 -} 1

                                            = 6^0.1 - 1

                                            = 1.1962 - 1

                                            = 19.62%

2 ) Calculation of future value :

           Future value = Present value *(1+r)ⁿ

                              = 1000 (1.16)^10

                              = 1000 * 4.4114

                              = $4411.40