Question

How much money has to be invested at 5.9% interest compounded continuously to have $15,000 after 12 years?

Answer 1

The amount of $7389.43 has to be invested at 5.9% interested continuously to have $15,000 after 12 years.

Step-by-step explanation:

The given is,

                Future value, F  = $15,000

                           Interest, i = 5.9%

              ( compounded continuously )

                            Period, t = 12 years

Step:1

           Formula to calculate the present with compounded continuously,

                                       $F=Pe^{(i)(t)}$...............(1)

           Substitute the values in equation (1) to find the P value,

                                  $15000=Pe^{(0.059)(12)}$          ( ∵ $i = \frac{5.9}{100}=0.059$ )

                                  $15000=Pe^{0.708}$

                                  $15000=P(2.0299)$             ( ∵ $e^{o.708} =2.0299$ )

            We change the P (Present value) into the left side,

                                        $P=\frac{15000}{2.0299}$

                                            $=7389.427$

                                            ≅ 7389.43

                                         P = $ 7389.43

Result:

           The amount of $7389.43 has to be invested at 5.9% interested continuously to have $15,000 after 12 years.