Question

PLEASE HELPPP ASAPPPP!!!!

Answer 1

To find how long it takes $500 to double if it is invested at 8% interest compounded semiannually, we can use the formula for compound interest:

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

Where:

A is the final amount (double the initial amount)

P is the principal (initial amount)

r is the interest rate (in decimal form)

n is the number of times the interest is compounded per year

t is the number of years

In this case, the initial amount (P) is $500, the interest rate (r) is 8% (or 0.08), and the interest is compounded semiannually (n = 2). We need to find the number of years (t) it takes for the amount to double (A = 2P).

Plugging in the values into the formula, we have:

2P = P(1 + r/n)^(nt)

2 = (1 + 0.08/2)^(2t)

Now, we can solve for t by taking the natural logarithm of both sides:

ln(2) = ln((1 + 0.08/2)^(2t))

Using properties of logarithms, we can bring the exponent down:

ln(2) = 2t * ln(1 + 0.08/2)

Now, we can solve for t by dividing both sides by 2 * ln(1 + 0.08/2):

t = ln(2) / (2 * ln(1 + 0.08/2))

Using a calculator, we can evaluate this expression to find the approximate value of t.

Remember to round the final answer to the nearest tenth as instructed.

Explanation:

Answer 2

To find how long it takes $500 to double with 8% interest compounded semiannually, use the formula A = P(1 + r/n)^(nt). It will take approximately 8.66 years.

To find how long it takes $500 to double if it is invested at 8% interest compounded semiannually, we can use the formula 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 the interest is compounded per year, and t is the number of years.

Using this formula, we can plug in the values: P = $500, r = 8% = 0.08, n = 2 (since it is compounded semiannually), and A = $1,000 (double the principal amount). We need to find t.

So the equation becomes: $1,000 = $500(1 + 0.08/2)^(2t).

Simplifying the equation, we get: 2 = (1.04)^(2t).

Next, we take the natural logarithm of both sides of the equation to solve for t.

t = ln(2) / (2 * ln(1.04)) ≈ 8.66 years.

The probable question may be:

Find how long it takes $500 to double if it is invested at 8% interest compounded semiannually. Use the formula

A=P(+t/n)^{nt} to solve the compound interest problem..

It will take approximately ____ years.

(Do not round until the final answer. Then round to the nearest tenth as needed.)