Question

Dave has $8000 to invest for 15 years. He finds a bank that offers an interest rate of 3.1% compounded monthly. How much money will he have after 15 years?

Answer 1

Dave will have $12,728 after 15 years, if he has $8000 to invest for 15 years. He finds a bank that offers an interest rate of 3.1% compounded monthly.

Step-by-step explanation:

The given is,

                 Investment = $ 8000

               No. of years = 15 years

             Interest rate, i = 3.1 %

                 ( compounded monthly )  

Step:1

          For for calculating future value with compound interest monthly,

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

         Where,

                     A = Future amount

                     P = Initial investment

                     r = Rate of interest

                    n = Number of compounding in a year

                     t = Time period

Step:2

           From given values,

                           P = $8000

                            r =  3.1%

                            t = 15 years

                            n = 12 ( for monthly)

           Equation (1) becomes,

                          $A = 8000( 1+\frac{0.031}{12} )^{(12)(15)}$

                              $= 8000 (1+0.002583)^{180}$

                              $= 8000(1.002583)^{180}$

                              $= 8000(1.591059)$

                              $=12728.48$

                           A = $ 12728.48

Result:

           Dave will have $12,728 after 15 years, if he has $8000 to invest for 15 years. He finds a bank that offers an interest rate of 3.1% compounded monthly.