find out how long it takes a $2700 investment to double if it is invested by 7% compounded semiannually. Round to the nearest tenth of a year . Use the formula A=P[1+r/n]^nt
how did you get (.035)
you want the $2700 to double, so A = 5400
5400 = 2700(1 + .035)^(2t)
2 = 1.035^(2t)
I hope you know how to use logs and know the rules of log operations
2t = log 2/log 1.035
2t = 20.148
t = 10.07
= 10.1 to the nearest tenth
seven percent/n= .07/2
Ah, the wonders of compound interest! Let Clown Bot work its magic to find out how long it takes for your investment to double.
Using the formula for compound interest, A = P[1 + (r/n)]^(nt), where:
A is the final amount,
P is the principal amount,
r is the annual interest rate,
n is the number of times interest is compounded per year, and
t is the number of years.
In this case, you want to find out t, so let's rearrange the formula a bit.
We start with the formula: A = P[1 + (r/n)]^(nt).
If you want to double your investment, then the final amount (A) should be 2 times the principal amount (P), i.e., A = 2P.
Therefore, we can rewrite the formula as: 2P = P[1 + (r/n)]^(nt).
By canceling P from both sides, we are left with: 2 = [1 + (r/n)]^(nt).
Now, let's plug in the given values:
P = $2700,
r = 7% = 0.07 (expressed as a decimal),
n = 2 (compounded semiannually),
and the unknown variable, t.
Thus, the equation becomes: 2 = [1 + (0.07/2)]^(2t).
Now it's time to solve for t. Let Clown Bot crunch the numbers to find the answer for you!
To find out how long it takes for a $2700 investment to double with a 7% interest rate compounded semiannually, we can use the formula for compound interest:
A = P[1 + (r/n)]^(nt)
Where:
A is the future value of the investment
P is the principal amount (initial investment)
r is the annual interest rate (converted to a decimal)
n is the number of times the interest is compounded per year
t is the number of years
Since we want the investment to double, the future value (A) will be twice the initial investment, so A = 2P.
We can set up the equation as follows:
2P = P[1 + (0.07/2)]^(2t)
Now we can solve for t.
Divide both sides by P:
2 = [1 + (0.07/2)]^(2t)
Take the logarithm of both sides to isolate the exponent:
log(2) = log([1 + (0.07/2)]^(2t))
Apply the logarithm property:
log(2) = 2t * log[1 + (0.07/2)]
Now, divide both sides by 2 * log[1 + (0.07/2)]:
t = log(2) / [2 * log(1 + (0.07/2))]
Using a calculator, we can evaluate this expression to find the value of t. Rounding to the nearest tenth of a year, we get:
t ≈ 9.9 years
Therefore, it will take approximately 9.9 years for the $2700 investment to double when compounded semiannually at a 7% interest rate.
2=(1+.07/2)^2t
log of both sides..
log2=2t log(1+.035)
can you do that? Solve for t?