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If you realized your investment account with semi-annual compounding periods (2 per year) had provided you with an effective annual rate of 14.6% over the last 21 years, what would you say its annual percentage rate would be? Your answer should be expressed as a percentage rounded to the 2nd place to the right of the decimal point

Respuesta :

The annual percentage rate of the investment account is of:

14.1%.

What is compound interest?

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

  • P is the principal, which is the value of deposit/loan/....
  • r is the interest rate, as a decimal value.
  • n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.

The effective annual interest rate is given as follows:

[tex]E = \left(1 + \frac{r}{n}\right)^n[/tex]

In this problem we have a semi-annual compounding, hence:

n = 2.

The effective rate was of 14.6%, hence E = 1.146, and thus the interest rate is obtained as follows:

[tex]E = \left(1 + \frac{r}{n}\right)^n[/tex]

[tex]1.146 = \left(1 + \frac{r}{2}\right)^2[/tex]

1 + 0.5r = 1.0705 (applying to square root to both sides).

0.5r = 0.0705

r = 0.0705/0.5

r = 0.141 = 14.1%.

More can be learned about compound interest at https://brainly.com/question/24274034

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