Question

Rebecca is currently working, but is planning to start a college in few years. For this purpose, she would need $20,000. Today she can start investing $750 monthly in an investment account that pays 6 percent compounded monthly. How long would it take her to have enough money to start college?

Answer 1

Rebecca would need to save money for approximately 22.25 years to have enough money to start college

Step-by-step explanation:

To calculate the time it would take for Rebecca to save enough money to start college, we can use the future value formula for compound interest:

FV = P(1 + r/n)^(nt), where

FV is the future value,

P is the principal (starting 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, P = $0, r = 6% or 0.06, n = 12 (compounded monthly), and FV = $20,000. Plugging these values into the formula, we get:

$20,000 = 0.06/12 * (1 + 0.06/12)^(12t)

To solve for t, we can use logarithms. First, divide both sides of the equation by $0.06/12:

$20,000 / ($0.06/12) = (1 + 0.06/12)^(12t)

Next, take the natural logarithm (ln) of both sides:

ln($20,000 / ($0.06/12)) = ln((1 + 0.06/12)^(12t))

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

ln($20,000 / ($0.06/12)) = 12t * ln(1 + 0.06/12)

Now, divide both sides by 12 * ln(1 + 0.06/12) to solve for t:

t = ln($20,000 / ($0.06/12)) / (12 * ln(1 + 0.06/12))

Using a calculator, t is approximately 22.25 years.

Therefore, it would take Rebecca around 22.25 years to have enough money to start college.