Nakiri invests $8,000 at age 18. She hopes the investment will be worth $64,000 when she turns 35. If the interest compounds continuously, approximately what rate of growth will she need to achieve her goal? Round to the nearest tenth of a percent.

Rate of interest is 12.232%, if Nakiri invests $8,000 at age 18 and she hopes the investment will be worth $64,000 when she turns 35.

Step-by-step explanation:

The given is,

                 Investment amount $8000 at age of 18

                 Future worth $64000 at age of 35

Step:1

               Formula to calculate the future amount with an interest of compounded continuously,

                                      ..........................(1)

              Where,

                         F - Future amount

                         P - Present amount

                          r - Rate of interest

                          t - No.of years  

             Constant, e = 2.7183    

             From given,

                       P = $8000        

                       F = $64000

                        t = 35-18 = 17 years

             Equation (1) becomes,

          Take log on both sides,

           Substitute log values of 8 and 2.7183

                        0.90308999 = ( r × 17 ) (0.4342974)

                              2.07942 = ( r × 17 )

                                          r = 12.232

Result:

            Rate of interest is 12.232%, if Nakiri invests $8,000 at age 18 and she hopes the investment will be worth $64,000 when she turns 35.

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