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Jill invests $7,972 in a retirement account with a fixed annual interest rate compounded continuously. After 15 years, the balance reaches
$16,876.72. What is the interest rate of the account?

Respuesta :

adioabiola

The interest rate of Jill's account as described is; 0.51%

The amount invested by Jill is $7,972.

According to compound interest;

  • A = P {1 + (r/n)}^nt.

In which case;

  • A = final amount = $16,876.72
  • P = principal amount = $7,972
  • r = interest rate = ?
  • n = number of times interest is compounded per time = 1
  • t = time = 15

Therefore;

  • $16,876.72 = $7,972 (1 + r/1)^(1×15)

  • $16,876.72/$7,972 = (1 + r/1)^(1×15)

  • 2.117 = (1 + r/1)^(1×15)

[tex]1 + r = \sqrt[15]{2.117} [/tex]

  • 1 + r = 1.051

  • r = 1.051 - 1

  • r = 0.051

The interest rate is therefore; 0.51%

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