Elizabeth brown wants to accumulate $8,000 by the end of 12 years. if the annual interest rate is 7.30 percent and interest compounded semi annually, how much will she have to invest today to achieve her goal?

She will invest approximately $3,383.97

Explanation:

Formula for compound interest:

                                 A  =  P(1 + r/n)^nt

Where:                      A  = Final amount

                                 P  =  Principal amount

                                 r   =  Interest rate

                                 n  =  Number of compounding periods per year

                                  t  =  Time period in years.

                                 A  =  $8,000

                                 P  =  Unknown

                                 r   =  7.30 percent   = 7.3% = 0.073

                                 n  =   semi annually = 2

                                  t  =   12 years

                         8,000  =  P(1 + 0.073/2)^2(12)

                         8,000  =  P(1 + 0.0365)^24

                         8,000  =  P(1.0365)^24

                         8,000  =  2.364086453P

Divide both sides by the coefficient of P

  8,000/2.364086453 =  2.364086453P/2.364086453

             3,383.971001  =  P

                                P   ≈  $3,383.97

That is Elizabeth Brown will invest approximately $3,383.97 to achieve her goal

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