Johnny invests $2,745 into an account, which has been earning interest for many years and he now has a total of $39,974. In two sentences explain why a negative number would be reasonable in the solution of the rate he received on his investment?

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Johnny invests $2,745 into an account, which has been earning interest for many years and he now has a total of $39,974. In two sentences explain why a negative number would be reasonable in the solution of the rate he received on his investment?

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Answer 1 · 2018-06-22T00:33:55

The "effective" annual interest rate may need to be reported.
Rearranging the formula for compound interest to find the effective interest rate would invoke a "negative" number in the equation.

Explanation:

Rearranging the formula for compound interest to find the effective interest rate would invoke a "negative" number in the equation.

$r = {(\frac{FV}{PV})}^{\frac{1}{n}} - 1$ $r = ("FV" /"PV")^(1/n) - 1$

$r = {(\frac{39974}{2745})}^{\frac{1}{n}} - 1$ $r = (39974/2745)^(1/n) - 1$

$r = {(14.562)}^{\frac{1}{n}} - 1$ $r = (14.562)^(1/n) - 1$

So, if the time lapse was 30 years, the rate would have been:
$r = {(14.562)}^{\frac{1}{30}} - 1 = 0.0932$ $r = (14.562)^(1/30) - 1 = 0.0932$ or $9.32 %$ $9.32%$

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Johnny invests $2,745 into an account, which has been earning interest for many years and he now has a total of $39,974. In two sentences explain why a negative number would be reasonable in the solution of the rate he received on his investment?

1 Answer

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