if shelia invested $5000 in an account paying 3% annual interest. how many years will it take her money to double? write it in exponential equation and rewrite it in log form. please help
I guess it is compound not simple interest.
2 = 1.03^n
log 2 = n log 1.03
n = log 2 /log 1.03 = 23.4 years
teachers answer is 2.58 years, can't figure this one out.
If your numbers are correct, 2.58 years makes no sense.
Nothing to figure out, md
Damon is correct and your teacher's answer is wrong.
We used to use an approximation formula called "the rule of 72"
To double your money, you simply multiply the rate by the number of years and you will get appr. 72
for Damon's answer: 23.4 * 3 = 70.2
looks very reasonable to me
To find out how many years it will take for Sheila's money to double in an account paying 3% annual interest, we can set up an exponential equation.
The formula for compound interest is given by:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, Sheila invested $5000 at an annual interest rate of 3%. We can assume that the interest is compounded annually (n = 1).
In order for Sheila's money to double, the future value (A) should be equal to 2 times the principal amount (P).
So, our exponential equation becomes:
2P = P(1 + r/n)^(nt)
Substituting the given values into the equation:
2(5000) = 5000(1 + 0.03/1)^(1t)
Simplifying the equation:
2 = (1.03)^t
To rewrite this equation in log form, we use the logarithm base and the power to isolate 't'.
log(2) = log((1.03)^t)
Using the logarithmic property log(a^b) = b * log(a):
log(2) = t * log(1.03)
Finally, to solve for 't', divide both sides of the equation by log(1.03):
t = log(2) / log(1.03)
Calculating t using a calculator or software:
t ≈ 23.45 years
So, it will take approximately 23.45 years for Sheila's money to double at a 3% annual interest rate.