Use properties of rational exponents to solve the compound interest formula for the interest rate, r. For the following exercises, use the compound interest formula, A(t) = P(1 + r/n)nt.

For the following exercises, use the compound interest formula, A(t) = P(1 + r/n)^nt.

Use properties of rational exponents to solve the compound interest formula for the interest rate, r.

Expert Solution

Consider the Compound Interest formula;

A(t) = P(1 + r/n)nt

Where, A(t) is the account value, “t” is the measured in years, “P” is the starting amount or initial value, “r” is the annual percentage rate (APR), “n” is the number of compounding periods in one year.

Use the compound interest formula to find the interest rate r;

A(t)/P = (1 + r/n)nt

Therefore,

{A(t)/P}1/nt = (1 + r/n)

Therefore,

{A(t)/P}1/nt – 1 = r/n

Therefore,

n × [{A(t)/P}1/nt – 1] = r

Therefore,

r = n × [{A(t)/P}1/nt – 1]

Therefore, the compound interest formula for the interest rate, r is r = n × [{A(t)/P}1/nt – 1].

Junaid answered 1 year ago

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Question

Use properties of rational exponents to solve the compound interest formula for the interest rate, r. For the following exercises, use the compound interest formula, A(t) = P(1 + r/n)nt.

Solutions

Expert Solution

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