How long it takes $800.00 to double if it is invested at 8% compounded quarterly?
800(1.02)^n = 1600 , where n is the number of quarter years
1.02^n = 2
n log 1.02 = log2
n = log2/log1.02 quarter years = ....
It says to use A=P(1+r/n)^nt
And to also round answer to 3 decimal places
Umhh ....
A=P(1+r/n)^nt
1600 = 800(1 + .08/4)^(4(t))
2 = (1.02)^4t
1.02^(4t) = 2 , look at my equation in my first reply.
Do you not have a calculator? Unless you have log tables from a 1980 textbook, you will need one.
To find out how long it takes for an investment to double, we need to use the compound interest formula:
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 the interest is compounded per year
t = the number of years
In this scenario, the initial investment (P) is $800.00, the annual interest rate (r) is 8% or 0.08 as a decimal, and the interest is compounded quarterly (n = 4). We want to find out the time it takes for the investment to double, so the future value (A) will be $1600.00 (which is twice the initial investment).
Let's plug in the values into the formula:
1600 = 800(1 + 0.08/4)^(4t)
Now, we can simplify the equation:
2 = (1 + 0.02)^(4t)
Taking the natural logarithm (ln) of both sides to solve for t:
ln(2) = ln(1.02)^(4t)
Using the logarithm property ln(a^b) = b * ln(a):
ln(2) = 4t * ln(1.02)
Now, we can solve for t:
t = ln(2) / (4 * ln(1.02))
Using a calculator, we can find that t is approximately 8.54 years.
Therefore, it will take about 8.54 years for $800 to double if it is invested at an 8% interest rate compounded quarterly.