Question

Thomas wants to save money for a vacation. Thomas invests $1,200 in an account that pays an interest rate of 4%.
How many years will it take for the account to reach $14,400? Round your answer to the nearest hundredth.

Answer 1

A=p{1+(r/n)}^nt where r is rate, n the number of compoundings per year and t the years.
14000=1200{1+.04/n}^nt We are not given the number of compoundings. I will assume 1.
14000=1200(1.04)^t
11.6667=1.04^t
logs of both sides
log 11.6667=t log 1.04
log11.6667/log 1.04 =t

1.067/.017=62.76 years
with continuous compounding
A=Pe^rt
11.6667=e^rt
ln of both sides
2.456=.04*t
t=61.40 years
Rule of 72, it would double in 18 years. Three doublings in 54 years, and four doublings in 72 years.
That would be 9600 in 54 years and 19,200 in 72 years, so the answer is between them, as it is.
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