Hi can someone check over my work?
Heather invested $2,000 at 7% compounded annually. How long, to three decimal places, will it take her investment to double?
\(\displaystyle \L\ A=I(1+i)^{n}\)
\(\displaystyle \L\ 4,000=2,000(1+0.70)^{n}\)
\(\displaystyle \L\ 2=1.70^{n}\)
\(\displaystyle \L\ log2=log1.70^{n}\)
\(\displaystyle \L\ log2=nlog1.70\)
\(\displaystyle \L\ \frac{log2}{log1.70}=n\)
\(\displaystyle \L\ 1.306=n\)
b) Heather used continuous compounding to estimate the doubling time in part a). How close were her estimates to the actual time?
\(\displaystyle \L\ A=Pe^{rt}\)
\(\displaystyle \L\ 4,000=2,000e^{0.70t}\)
\(\displaystyle \L\ 2=e^{0.70t}\)
\(\displaystyle \L\ log2=loge^{0.70t}\)
\(\displaystyle \L\ log2=0.70tloge\)
\(\displaystyle \L\frac{log2}{(loge)0.70}=t\)
\(\displaystyle \L\ 0.990=t\)
1.306-0.990=0.316 years off
Thanks
Heather invested $2,000 at 7% compounded annually. How long, to three decimal places, will it take her investment to double?
\(\displaystyle \L\ A=I(1+i)^{n}\)
\(\displaystyle \L\ 4,000=2,000(1+0.70)^{n}\)
\(\displaystyle \L\ 2=1.70^{n}\)
\(\displaystyle \L\ log2=log1.70^{n}\)
\(\displaystyle \L\ log2=nlog1.70\)
\(\displaystyle \L\ \frac{log2}{log1.70}=n\)
\(\displaystyle \L\ 1.306=n\)
b) Heather used continuous compounding to estimate the doubling time in part a). How close were her estimates to the actual time?
\(\displaystyle \L\ A=Pe^{rt}\)
\(\displaystyle \L\ 4,000=2,000e^{0.70t}\)
\(\displaystyle \L\ 2=e^{0.70t}\)
\(\displaystyle \L\ log2=loge^{0.70t}\)
\(\displaystyle \L\ log2=0.70tloge\)
\(\displaystyle \L\frac{log2}{(loge)0.70}=t\)
\(\displaystyle \L\ 0.990=t\)
1.306-0.990=0.316 years off
Thanks
