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Nu-Tools plans to set aside an equal amount of money each year, starting today, so that it will have $25,000 saved at the end of three years. If the firm can earn 4.7 percent, how much does it have to save annually

Respuesta :

Edufirst

Answer:

    [tex]\large\boxed{\large\boxed{\$7,596.61}}[/tex]

Explanation:

The future value of an equal amoount of money invested each year, starting today, is calculated with the formula for an annuity with payments made at the beginning of each period.

The formula is:

        [tex]Future\text{ }value=Annuity\times \bigg[\dfrac{(1+r)^t-1}{r}\bigg]\times (1+r)[/tex]

Where:

  • Annuity is the equal amount of money invested each year, starting today
  • Future valueis the money that you will have saved at the end of the period: $25,000
  • r is the annual rate: 4.7% = 0.047

Substitute solve for the annuity:

      [tex]\$25,000=Annuity\times \bigg[\dfrac{(1+0.047)^3-1}{0.047}\bigg]\times (1+0.047)[/tex]

      [tex]\$25,000=Annuity\times 3.29093982[/tex]

     [tex]Annuity=\$25,000/3.29093982=\$7,596.61[/tex]

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