Question

What is the time required for $2500 to amount to $3000 at 6% compounded quarterly

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the time required for $2500 to amount to $3000 at 6% compounded quarterly, we can use the formula for compound interest:

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

Where:
A = the resulting amount
P = principal amount (starting amount)
r = interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years

In this case,
P = $2500
A = $3000
r = 6% = 0.06 (as a decimal)
n = 4 (compounded quarterly)

Let's substitute the known values into the formula and solve for t:

3000 = 2500(1 + 0.06/4)^(4t)

Divide both sides by 2500:

1.2 = (1 + 0.06/4)^(4t)

Take the natural logarithm (ln) of both sides:

ln(1.2) = ln[(1 + 0.06/4)^(4t)]

ln(1.2) = (4t) ln(1 + 0.06/4)

Divide both sides by ln(1 + 0.06/4):

(4t) = ln(1.2) / ln(1 + 0.06/4)

t = [ln(1.2) / ln(1 + 0.06/4)] / 4

Using a calculator, we find:

t ≈ 3.89

Thus, the time required for $2500 to amount to $3000 at 6% compounded quarterly is approximately 3.89 years.