Question

Use the compound interest formula A =​P(1 + ​r) t and the given information to solve for r.

Answer 1

Answer:

Rounding to nearest hundredths gives us r=0.06.

So r is about 6%.

Step-by-step explanation:

So we are given:

$A=P(1+r)^t$

where

$A=2300$

$P=1600$

$t=6$.

$A=P(1+r)^t$

$2300=1600(1+r)^6$

Divide both sides by 1600:

$\frac{2300}{1600}=(1+r)^6$

Simplify:

$\frac{23}{16}=(1+r)^6$

Take the 6th root of both sides:

$\sqrt[6]{\frac{23}{16}}=1+r$

Subtract 1 on both sides:

$\sqrt[6]{\frac{23}{16}}-1=r$

So the exact solution is $r=\sqrt[6]{\frac{23}{16}}-1$

Most likely we are asked to round to a certain place value.

I'm going to put my value for r into my calculator.

r=0.062350864

Rounding to nearest hundredths gives us r=0.06.