Question

Suppose that a young couple has just had their first baby and they wish to ensure that enough money will be available to pay for their child's college education. Currently, college tuition, books, fees, and other costs average $20,000 per year. On average, tuition and other costs have historically increased at a rate of 6% per year. Assuming that college costs continue to increase an average of 6% per year and that all her college savings are invested in an account paying 8% interest, then the amount of money she will need to have available at age 20 to pay for all four years of her undergraduate education is closest to ________.

Answer 1

To calculate the required savings for a child's future college education, project the future cost of tuition by applying a 6% annual growth rate and then find the present value using an 8% discount rate. Add up the present value of each year's projected tuition to get the total amount needed.

Step-by-step explanation:

To calculate the amount of money needed for a child's college education 20 years from now, we must first project the future cost of college and then determine the present value of that cost to find out how much should be saved today. The future cost of college can be estimated by applying the historical average increase in tuition and other costs.

Step 1: Projecting the Future Cost of College

The future cost of college is calculated using the formula for compound interest: Future Value = Present Value * (1 + growth rate)^number of years. For each year of college 20 years from now, we will need the following:

• Year 1: $20,000 * (1 + 0.06)^20
• Year 2: $20,000 * (1 + 0.06)^21
• Year 3: $20,000 * (1 + 0.06)^22
• Year 4: $20,000 * (1 + 0.06)^23

After calculating each year's cost, we sum them up to get the total future cost of the education.

Step 2: Calculating the Present Value

Next, we find the present value of the total future cost using the formula: Present Value = Future Value / (1 + discount rate)^number of years. The discount rate is 8% (the interest rate at which the college savings would grow).

By performing these calculations, we can determine the approximate amount that needs to be saved today to cover the projected costs of a four-year college education 20 years from now.

Answer 2

$256,571

Step-by-step explanation:

College Graduation fee for four years in the present value

PV = $20,000 x 4 = $80,000

As historically the fee has risen by 6% we need to find future value when the baby will be 20 years old by using future value formula

Let's say

FV = Future value

PV = Present value

n = number of years

i = Interest

Workings

FV = PV x ((1+growth rate)^n)

FV = $80,000 x ( (1+0.06)^20)

FV = $256,571

As the bank interest rate is 8% the saving need to be deposited annualy can be calculated as

Savings = (FV x i) / ((1+i)^n)-1)

Savings = ($256,571 x 0.08) / ((1+0.08)^20)-1)

Savings = 20,525.68 / 3.66

Savings = $5,608