Question

A wise investor purchased a plot of land in 1947 for $84 000. In 1987 that same investor sold the land for $49 000 000?

what annual rate of interest corresponds to an investment of $84 000 which grows to $49 000 000 in 40 years?


(logarithms)

Answer 1

so that is where it came from

Answer 2

lol

Answer 3

not really a log problem

Answer 4

i didn't think so but its art of the log q's in my book

Answer 5

you want to solve
\[4900=84(1+x)^{40}\] for x

Answer 6

divide by 84
take the 40th root (with a calculator)
subtract 1

Answer 7

\[\frac{175}{3}=(1+x)^{40}\]
\[\sqrt[40]{\frac{175}{3}}=1+x\]
\[

Answer 8

that dude made some crazy cash

Answer 9

i get
\[x+1=1.107\]
\[x=.107=10.7\%\]

Answer 10

thisis the answer in my book.. i just don't know how they got it..
\[49 000 000\div84 000000= (1+x)^{40}\]
\[(1750 \div 3) ^{1/40) = 1+x

(\[1730\div3^{1/40}\]-1=x

0.1726\[approxx\]

Answer 11

i wrote it out yes? still confused let me know

Answer 12

where do u get 175 and 3

Answer 13

oh from reducing the fraction

Answer 14

4900/84

Answer 15

how do you do that

Answer 16

i have forgotten all of my middle school math

Answer 17

what i mean is how do u know when to stop reducing

Answer 18

You can use logarithms to solve this
A=P.e^rt
A=value, P=original amount, r=interest rate, t=time, and e=e=2.71828
49million=84,000 x e^R.40
ln(49000/84)=ln(e^R.40)
ln(49000/84)=40 x R
R = 6.36/40 = 1.59
Look up "natural logarithm"

Answer 19

When we didn't have calculators, finding the 40th roots of things was difficult. ;-)