Question

Marcy received an inheritance of $20,000 and invested it at a 6% interest. She is going to use it for college, withdrawing money for tuition and expenses each quarter. How much can she take out each quarter if she has 3 years of school left?

Answer 1

Marcy can withdraw approximately $1,856.58 each quarter from her $20,000 inheritance invested at 6% interest to cover her expenses for 3 years of college.

Step-by-step explanation:

Marcy plans to use her inheritance of $20,000 invested at 6% interest to finance her college tuition and expenses. To determine how much she can withdraw each quarter, we need to calculate the annuity payments for a 3-year period, assuming four quarters per year, totaling 12 quarters.

Firstly, we need to find the quarterly interest rate by dividing the annual rate by the number of quarters per year:

Quarterly interest rate

= 6% / 4 = 1.5% or 0.015 in decimal form.

Next, we use the annuity payment formula which is:

PMT = PV * (r/(1-(1+r)^(-n)))

Where PMT is the payment per period, PV is the present value (her inheritance), r is the interest rate per period, and n is the total number of payments.

Plugging in Marcy's values, we have:

PMT = $20,000 * (0.015/(1-(1+0.015)^(-12)))

After solving, we get:

PMT = $20,000 * (0.015/(1-(1.015)^(-12)))

PMT ≈ $20,000 * 0.09283

PMT ≈ $1856.58

So, Marcy can withdraw approximately $1,856.58 each quarter to pay for her college education.