Question

Clara invests $5,000 in an account that pays 6.25% interest per year. After how many years will her investment be worth $10,000?

Answer 1

I'm thinking 11.4 years?

Answer 2

you need to solve
\[10,000=5,000(1.0625)^y\] for \(y\) first step is divide by 5,000 and solve
\[2=(1.0625)^y\]

Answer 3

we will use the formula A=P(1+r)^n where A=10000 P=5000 and r = 0.0625

Answer 4

you solve for a variable in the exponent via
\[b^x=A\iff x=\frac{\ln(A)}{\ln(b)}\] so you need to compute
\[\frac{\ln(2)}{\ln(1.0625)}\]

Answer 5

Okay will do

Answer 6

looks like you did it already since your answer is right