Question

How to find compound rate from given values, 10 years after, and initial

Answer 1

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

How to determine the compound interest rate?

The compound interest formula is:

$I = P(1 + \frac rn)^{nt} - P$

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

$P + I = P(1 + \frac rn)^{nt}$

Divide through by P

$\frac{P + I}{P} = (1 + \frac rn)^{nt}$

Take the nt-th root of both sides

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

Subtract 1 from both sides

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

Multiply through by n

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

In this case, t = 10

So, we have:

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

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

Read more about compound interest at:

brainly.com/question/13155407

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