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Assume the total cost of a college education will be $325,000 when your child enters college in 18 years. You presently have $85,000 to invest. What annual rate of interest must you earn on your investment to cover the cost of your child's college education? Input area: (Use cells A6 to B8 from the given information to complete this question.)

User Nicomp
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2 Answers

3 votes

Final answer:

The annual rate of interest needed can be found using the compound interest formula. By assuming annual compounding, the formula simplifies and allows for algebraic solving after setting up with given values. Compound interest enables significant growth of investments over time, imperative for covering rising college costs.

Step-by-step explanation:

To find out the annual rate of interest needed to grow your current investment of $85,000 to cover the total future cost of a college education of $325,000 in 18 years, you can use the compound interest formula:

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

Where:

  • A is the amount of money accumulated after n years, including interest.
  • P is the principal amount (the initial amount of money).
  • r is the annual interest rate (decimal).
  • n is the number of times that interest is compounded per year.
  • t is the time the money is invested for in years.

Since the question does not specify how often the interest is compounded, we will assume it is compounded annually (n=1). Therefore, the formula simplifies to:

A = P(1 + r)^t

Let's set up the equation with the given values:

325000 = 85000(1 + r)^18

To solve for r, the annual interest rate, you'll divide both sides by 85,000 and then take the 18th root of the result to isolate (1 + r):

(325000 / 85000) = (1 + r)^18

You would then use a financial calculator or algebraic methods to solve for r.

Compound interest is a powerful tool in finance, allowing money to grow over time. As illustrated by the example provided, even modest investments can grow significantly when left to compound. Preparing for future college costs through wise investments is essential, as evident from the rise in tuition and other expenses over the years.

User Mohamed Mahdi
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7 votes

The annual rate of interest required to grow an investment from $85,000 to $325,000 over 18 years is approximately
\( 7.74\% \).

How to get the annual rate of interest

The formula to solve for this is given as:


\[ A = P(1 + r)^n \]

When we put in the formula we have


\[ \$325,000 = \$85,000(1 + r)^(18) \]

we have to rearrange to get r


\[ 1 + r = \left( (\$325,000)/(\$85,000) \right)^{(1)/(18)} \]


\[ 1 + r = \left( (325000)/(85000) \right)^{(1)/(18)} \]


\[ 1 + r = \left( 3.82353 \right)^{(1)/(18)} \]


\[ 1 + r = 1.07736 \]

subtract 1 from bith sides of the equation


\[ r =1.07736 - 1 \]


\[ r = 0.07736 \]

= 7.74&

User Jakim
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