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In 2 years, you want to have $5000 in your savings account. Find the amount you should deposit if the account pays 3% annual interest, compounded monthly. Round your answer to the nearest cents and make sure you do not type the dollar sign($) in your answer.

Respuesta :

Ashraf82

The amount you should deposit is $4709.18

Step-by-step explanation:

The formula for compound interest, including principal sum is

[tex]A=P(1+\frac{r}{n})^{nt}[/tex] , where:

  • A is the future value of the investment/loan, including interest
  • P is the principal investment amount
  • r is the annual interest rate in decimal
  • n is the number of times that interest is compounded per unit t
  • t is the time the money is invested or borrowed for

∵ You want to have $5000 in your savings account in 2 years

∴ A = 5000

∴ t = 2

∵ The account pays 3% annual interest, compounded monthly

∴ r = 3% = 3 ÷ 100 = 0.03

∴ n = 12 ⇒ compounded monthly

- Substitute these values in the formula above

∴ [tex]5000=P(1+\frac{0.03}{12})^{(12)(2)}[/tex]

∴ [tex]5000=P(1+0.0025)^{24}[/tex]

∴ [tex]5000=P(1.0025)^{24}[/tex]

- Divide both sides by [tex](1.0025)^{24}[/tex]

∴ P = 4709.18

The amount you should deposit is $4709.18

Learn more:

You can learn more about the compounded interest in brainly.com/question/2514241

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