Question

Find how long it will take a $5000 investment to grow to $10,000 if it is invested at 8% interest compounded quarterly.. a=p(1+r/n)^nt

Answer 1

Take the time as x. Make both the bases equal and solve it.

Answer 2

\[10,000=5,000(1+\frac{.08}{4})^{4t}\]
\[2=(1.002)^{4t}\]
\[4t=\frac{\ln(2)}{\ln(1.002)}\]

\[t=\frac{\ln(2)}{4\ln(1.002)}\] then a calculator

Answer 3

how did you do step 3? i know ln, but how did the2 move over?

Answer 4

step 1: divide by 5,000
step 2: you solve
\[b^x=A\] for x via
\[x=\frac{\ln(A)}{\ln(b)}\] by the "change of base formula"

Answer 5

step 3: divide by 4

Answer 6

Thanks.