invest money that pays 6.3% interest/year compounded quarterly.

How long should invest if want to double initial investment?

LAURA INVESTED $5000 AT 3% COMPOUNDED SEMIANNUALLY.IN HOW MANY YEARS WILL LAURAS INVESTEMENT HAVE DOUBLE?

To determine how long you should invest in order to double your initial investment, you can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:
A = Total amount after time t
P = Principal or 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, your principal investment will double, so the total amount (A) will be 2P. The interest rate (r) is 6.3% per year, which is equivalent to 0.063 as a decimal. The interest is compounded quarterly, so n = 4. Now we can solve for t:

2P = P(1 + 0.063/4)^(4t)

Dividing both sides by P, we get:

2 = (1 + 0.063/4)^(4t)

Take the natural logarithm (ln) of both sides to isolate the exponent:

ln(2) = ln[(1 + 0.063/4)^(4t)]

Now, divide both sides by 4:

ln(2)/4 = t ln[(1 + 0.063/4)]

Finally, divide ln(2)/4 by ln[(1 + 0.063/4)] to solve for t:

t = ln(2)/[4 * ln(1 + 0.063/4)]

Using a calculator, you can find the value of t for this equation. The result will give you the approximate number of years needed to double your initial investment at a 6.3% interest rate compounded quarterly.