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MrRoyal

The formula that calculates the compound rate from the given values is [tex]r = n(-1 + \sqrt[10n]{\frac{P + I}{P}})[/tex]

How to determine the compound interest rate?

The compound interest formula is:

[tex]I = P(1 + \frac rn)^{nt} - P[/tex]

Where:

  • P represents the principal amount
  • r represents the compound interest rate
  • n represents the number of times the interest is compounded
  • t represents the time in years
  • I represents the interest

We start by adding P to both sides

[tex]P + I = P(1 + \frac rn)^{nt}[/tex]

Divide through by P

[tex]\frac{P + I}{P} = (1 + \frac rn)^{nt}[/tex]

Take the nt-th root of both sides

[tex]\sqrt[nt]{\frac{P + I}{P}} = 1 + \frac rn[/tex]

Subtract 1 from both sides

[tex]-1 + \sqrt[nt]{\frac{P + I}{P}} = \frac rn[/tex]

Multiply through by n

[tex]r = n(-1 + \sqrt[nt]{\frac{P + I}{P}})[/tex]

In this case, t = 10

So, we have:

[tex]r = n(-1 + \sqrt[10n]{\frac{P + I}{P}})[/tex]

Hence, the formula that calculates the compound rate is [tex]r = n(-1 + \sqrt[10n]{\frac{P + I}{P}})[/tex]

Read more about compound interest at:

https://brainly.com/question/13155407

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