Question

Four years ago, Saul invested $500. Three years ago, Trek invested $600. Today, these two investments are each worth $800. Assume each account continues to earn its respective rate of return. Which one of the following statements is correct concerning these investments?A) One year ago, Saul's investment was worth less than Trek's investment. B) Three years from today, Trek's investment will be worth more than Saul's. C) Trek earns a higher rate of return than Saul. D) Trek has earned an average annual interest rate of 9.86 percent. E) Saul has earned an average annual interest rate of 12.64 percent.

Answer 1

Answer:

A) One year ago, Saul's investment was worth less than Trek's investment. B)

Explanation:

Computation of Saul's Investment Rate of Interest

                                 A  =  P(1 + r)^t

Where:                     A  = Final amount

                                P  =  Principal amount

                                r   =  Interest rate

                                t  =  Time period in years.

                                A  =  $800

                                P  =  $500

                                r   =  Unknown

                                 t   =   4 years

                            800  =  500(1 + r)^4

Divide both sides by 500

                     800/500 =  (500(1 + r)^4 )/500

                               1.6  =  (1 + r)^4

Take the fourth root of both sides

                           $\sqrt[4]{1.6}$ = $\sqrt[4]{1 + r)^4}$

          1.1246826504  =  (1 + r)

          1.1246826504  =  1 + r

Subtract 1 from both sides

      1.1246826504 - 1  =  1 -1+ r

           0.1246826504  =  r

Convert 0.1246826504 to percentage and to 2 decimal places

                                   r = 12.47%

That is, Saul investment is at 12.47% interest rate

Computation of Trek's Investment Rate of Interest

                                A  =  $800

                                P  =  $600

                                r   =  Unknown

                                 t   =   4 years

                            800  =  600(1 + r)^4

Divide both sides by 600

                     800/600 =  (600(1 + r)^4 )/600

              1.333333333  =  (1 + r)^4

Take the cube root of both sides

              $\sqrt[3]{1.333333333}$ = $\sqrt[3]{1 + r)^4}$

              1.100642416 =  (1 + r)

             1.100642416  =  1 + r

Subtract 1 from both sides

         1.100642416 - 1  =  1 -1+ r

             0.100642416  =  r

Convert   0.100642416 to percentage and to 2 decimal place

                                 r = 10..06%

That is, Trek investment is at 10..06% interest rate

It can be observed that Saul earns a higher rate of return than Trek. The fact that both investment have equal returns today, it means Saul's investment was worth less than Trek's investment one year ago.