Any math geniuses out there?

Question

i have to do a project but i could not solve the last question
can anyone help me?

determine the compund interest rate at which 7200 euro grows to 9000 euro in 15 years. (Give your answer as a percentage to one decimal place).,

Please do not just give the answer, show your working. cause i want to learn how to solve it
the formula is An = (1 plus r/100)^n

thanks

Answer 1

You have the formula, it's pretty much plug 'n play.
9000 = 7200*(1+r)^15 so
1.25 = (1+r)^15 and, taking the log of both sides
log(1.25) = 15*log(1+r) so
log(1.25)/15 = log(1+r) and
10^(log(1.25)/15) = 1+r or
r = 10^(log(1.25)/15) - 1 Now dig out a calculator
r = 1.498 %

HTH

Doug

Answer 2

A = Future Value
P = Present value
i = r/100 annual interest rate in decimal form
n = number of years

A = P(1+i)^n
log A = logP + nlog(1+i)
log(1+i) = (log A - log P) / n
substitute your numbers
log(1+i) = (log9000 - log7200)/5 = .01938200
so
1+i = 10^.01938200 = 1.0456
i = 1.0456 - 1 = .0456 = r/100
so r = about 4.6%

Answer 3

I learned that

9000=7200e^(r15) where r is the rate of interest in decimal form. e is a math constant that equals 2.718 (like pi=3.14).

so, 9000/7200=1.25 leaving 1.25=e^r15
make both of these ln...ln1.25=15rlne
lne=1 so to get r just divide ln1.25 by 15 and you get .01487
that means your interest rate is 1.48%

Answer 4

wat?