## The Math Behind Saving Money to Pay Your Child's College Tuition

written by: John Garger•edited by: Wendy Finn•updated: 12/2/2011

Knowing how much to save for your child’s college education can seem like a complicated matter. However, it is really just an application of the time value of money. Sounds complicated? Don't worry we'll walk you through it with some formulas to help you work out those crucial figures.

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### When? How Much!

It is no secret that the earlier parents start saving for their child’s education, the easier it will be to ensure that the money needed to pay for college will be ready and waiting. However, what gives many parents trouble in saving for their child’s future college tuition is the actual amount that must be put away each month. Simple arithmetic is not enough because parents must often start saving years, if not decades, in advance. Such variables as inflation and interest earned on money saved, makes the calculation a bit more complicated than arithmetic can handle.

Money today is not the same as money tomorrow, or even yesterday for that matter. Essentially, the value of money changes over time because of risk and a devaluation of currency known as inflation. For our purposes here, inflation can be defined as the eroding of the value of currency in direct proportion to the amount of money in circulation in an economy. The more money in circulation, the less each unit of currency is worth. Of course, many economic factors contribute to inflation, but for the purposes of saving for college, the effects of inflation are more important than its causes.

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### An Example Situation

Suppose that a parent has just had a child and the parent wants to begin saving for the child’s college education immediately. Let us assume that the child will enter college at age eighteen and will pursue a Bachelor’s Degree for four years. The parent now knows that he/she has eighteen years to save for the tuition. Let us further assume that a college education today costs \$8,000 per year. Therefore, the total college tuition will amount to \$32,000 (8,000 * 4).

The first problem to tackle is inflation. The time value of money tells us that money today is not the same as money tomorrow. It is not that the tuition will be higher in eighteen years, it’s that the money will be worth less. Therefore, we need more of it to purchase the same product. We need to know the future value of a college education today eighteen years into the future. Let us assume that the average inflation rate is about 2% per year. We cannot simply multiply 2% by eighteen years because previous year’s inflation compounds in each successive year. The Future Value formula can be stated as:

FV = PV * (1 + r)n

Where FV is the future value, PV is the present value, r is an interest, discount, or inflation rate, and n is the number of periods. Using this formula, we find that the future value of a \$32,000 college education is:

FV = 32,000 * (1 + 0.02)18

FV = 32,000 * 1.4282

FV = \$45,703.88

So, the parent needs to have about \$45,704 in eighteen years to pay for his/her child’s college education.

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### How Much to Save Each Month

The last part of the equation is to figure out how much money the parent needs to put away each month over the next eighteen years to arrive at the \$45,704 figure. The first variable to assess is the interest rate the money will accrue over the next eighteen years. Certainly, the parent could place the money in a non-interest bearing savings account but given the length of time until the money is needed, far less needs to be put away each month if the money earns even a little interest. It is beyond the scope of this article to discuss these options in detail, but many banks offer savings accounts specifically designed for those saving for college. Parents may opt to invest in Certificates of Deposit, 529 plans, or other investment opportunities. For our purposes here, let us assume that whatever investment plan the parent chooses, it is expected to pay 5% APR with monthly compounding. If the interest rate is quoted as an APY, a conversion to an APR must be calculated.

The simple future value formula above assumes that the college tuition is needed all at once. In contrast, monthly saving can be thought of as an annuity payment because a fixed amount of money is continually paid into some investment, and previous interest earns interest in subsequent periods. Therefore, we can use the future value of an annuity formula to calculate the monthly payment needed to save \$45,704 over eighteen years at 5% APR interest. The future value of an annuity formula is given as:

FVA = CF * [(((1 + r)n) – 1) / r]

Where FVA is the future value of the annuity, CF is the recurring cash flow (monthly saving), r is the interest rate, and n is the number of periods. In this case, the cash flow is the amount that needs to be saved each month. Also, since interest is calculated monthly, the number of periods will be 216 (18 * 12) since the parent will be contributing to the college fund 216 times over the next eighteen years. We also need to divide the annual interest rate by 12 to find the monthly interest rate. In this case, the monthly interest rate is 0.004167 (0.05 / 12). Using the formula above, we find that:

45,704 = CF * [(((1 + 0.004167)216) – 1) / 0.004167]

45,704 = CF * 349.20

CF = \$130.88

So, the parent must put away \$130.88 per month for the next 216 months (eighteen years) at an interest rate of 5% APR to save the \$45,704 needed for the child’s education. Notice that because of the interest earned, the parent only needed to actually save \$28,270.08 (130.88 * 216). The remaining \$17,434.92 was the result of interest! As you can see, the power of compounding interest makes saving early for college worthwhile.

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### The Power of Interest - Thinking About the Future

The example above is a somewhat simple representation of the power of interest when saving for college. Understand that there are a few assumptions left out of this example. It was completely ignored that the parent does not need all of the money when the child enters college. Some money can also be saved over the course of the four years while the child is attending college. Also, inflation is not always as predictable as assuming it will be a flat percentage each year; that is only an approximation.

In addition, it is assumed that no major changes will occur in the college industry. For example, perhaps by the time eighteen years go by all college students will be enrolled in online colleges, which may change the pricing structure. Perhaps college education will no longer be necessary in the future or perhaps college education prices will decrease.

All of these possibilities are a part of good financial planning. It is a factor of risk management; are the assumptions above in calculating the amount needed likely to hold over eighteen years? Can the parent assume that the 5% will be attainable in the long term? These qualitative factors cannot be easily expressed in a time value of money equation. Consequently, financial planning for college requires more than a calculation of monthly payments, inflation, and interest rates.