# Growing Interest Rate Specified

How long will it take for $400 to grow to $1000 at the interest rates specified?

a. 4%

b. 8%

c. 16%

Please show all work.

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#### Solution Preview

One period gives the principal multiplied by the factor (1 + x%/100) for brevity x%/100 =x where x is the correspondent fractional percent.

In the next period the new principle is P(1 +x) and at the end of the period we obtain this multiplied again by (1+x) So for n periods the new principle returned is P(1+x)^n

So now we want $400 to return as $1000 in n ...

#### Solution Summary

The solution gives the formulas, the explanations and a proof for the problems.

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