Question

lucy invests $800 in an account that earns 6.12% annual interest compounded continuously. juan invests $1600 in an account that earns 3.9% annual interest compounded continuously. find when the value of lucys investment equals the value of juans investment?

Answer 1

Answer:

Both their investments will reach a similar value in 32 years, 9 months and 8 days. Both accounts will have exactly $5,606.

Explanation:

Original investment:              $800 at 6.12%                    $1,600 at 3.9%          

future value 10 years                     $1,449                                $2,346

future value 20 years                   $2,624                                $3,439

future value 30 years                   $4,753                                $5,042

future value 31 years                    $5,044                                $5,238

future value 32 years                   $5,353                                $5,442

future value 33 years                   $5,681                                 $5,655

It will take over 32 years for both investments to match their amounts.

to determine the approximate month we start with the future value in 32 years:

                                                         $5,353                          $5,442

future value in 6 months                 $5,517                           $5,548

future value in 9 months                $5,599                           $5,601

future value in 9 months                                                                          

and 5 days                                      $5,603                           $5,604

future value in 9 months                                                                          

and 8 days                                      $5,606                           $5,606