Question

A person invests 9000 dollars in a bank. The bank pays 4.25% interest compounded daily. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 19600?

Answer 1

The person must invest the money in the bank for 18 years to reach $19600, if a person invests 9000 dollars in a bank and the bank pays 4.25% interest compounded daily.

Step-by-step explanation:

The given is,

                       A person invests 9000 dollars in a bank      

                      The bank pays 4.25% interest compounded daily

                      Future amount $19600

Step:1

                     Formula to calculate the future investment with compounded daily,

                                                  $A = P (1+\frac{r}{n})^{nt}$................................(1)

                   Where, A - Future amount

                                P - Initial investment

                                r - Interested rate

                                n - No.of times for a year

                                t - No.of years

Step:2

              From the given values,

                      A = $ 19600

                      P = $ 9000

                       r = 4.25 %

                      n = 365  ( ∵ Compounded daily )

           Equation (1) becomes,

                                        $19600 = 9000(1+\frac{0.0425}{365})^{365t}$

                                         $\frac{19600}{9000}= (1+0.000116438)^{365t}$

                                   $2.177778=(1.000116438)^{365t}$

            ( Take log on both sides )

                               $log 2.17778= log (1.000116438)^{365t}$

                               $log 2.17778=( 365t)log (1.000116438)$

           Substitute the log values,

                                  $0.338014 = (365t)(0.000050565)$

                                $\frac{0.338014}{0.000050565}= 365t$

                                $6684.6842 = 365t$

                                              $t = \frac{6684.6842}{365}$

                                                 = 18.314

                                                 ≅ 18 years

                          No.of years, t = 18 years

Result:

              The person must invest the money in the bank for 18 years to reach $19600, if a person invests 9000 dollars in a bank and the bank pays 4.25% interest compounded daily.