Question

A bank advertises that it compounds money quarterly and that it will take Double your money in 10 years. what is the interest-rate?

Answer 1

The interest rate is 6.992%, if a bank advertises that it compounds money quarterly and that it will take Double your money in 10 years.

Step-by-step explanation:

The given is,

                          Compounds money quarterly

                          Double your money in 10 years

Step:1

              Formula to calculate future investment with compounded quarterly,

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

              Where, A - Future amount

                           P - Initial investment\

                            r - Rate of interest

                            n - No. of compounding in a year

                             t - No. of years

Step:2

               Let, P = X

                      A = 2X ( Double your money )

              From given, n - 4 ( for compounding quarterly )

                                    t - 10 years

               From equation (1)

                                                        $2X =X(1+\frac{r}{4} )^{(4)(10)}$

                                                         $\frac{2X}{X} =(1+\frac{r}{4} )^{(4)(10)}$

                                                            $2 =(1+\frac{r}{4} )^{40}$

          Take root $40^{th}$ root on both side,

                                                         $\sqrt[40]{2} = (1+\frac{r}{4} )$

                                            $1.017479692 = (\frac{4+r}{4} )$

                                     $(1.017479692)(4) = (r+4)$

                                                  $4.06992=(r+4)$

                                                              $r = 4.06992 -4$

                                                              $r =( 0.06992)(100)$

                                                              r = 6.992 %

Result:

             The interest rate is 6.992%, if a bank advertises that it compounds money quarterly and that it will take Double your money in 10 years.