Question

tims grandparents want to help his parents with a 529 college-savings plan. the accound grows tax-free. they want the plan to grow to $50,000 over 18 years. if the account will earn 6% compounded semi-annually (twice a year), to the nearest dollar. how much will tims grandparents need to invest in the account now?

Answer 1

Answer: $22,643

Explanation:

To calculate how much Tim's grandparents need to invest in the account now, we can use the formula for compound interest:

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

Where:

A is the future value of the account (which is $50,000 in this case),

P is the principal amount (the initial investment we want to find),

r is the annual interest rate (6% in this case),

n is the number of times the interest is compounded per year (twice a year, so n = 2),

and t is the number of years (18 years in this case).

Let's plug in the given values and solve for P:

$50,000 = P(1 + 0.06/2)^(2 * 18)

Simplifying the equation further:

$50,000 = P(1 + 0.03)^(36)

$50,000 = P(1.03)^36

To find the value of P, divide both sides of the equation by (1.03)^36:

P = $50,000 / (1.03)^36

Using a calculator, we find that (1.03)^36 is approximately 2.2049.

P = $50,000 / 2.2049

P ≈ $22,643

Therefore, Tim's grandparents need to invest approximately $22,643 in the account now to achieve a future value of $50,000 over 18 years with a 6% annual interest rate compounded semi-annually.