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# Present Value of Growing Annuity

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Jane has a child and wishes to begin saving for college expenses. Child will enter college in 6 years. Assume child will spend 4 years in college, that the real (ie: inflation adjusted) annual cost of a college education will remain at \$24,000, that the nominal interest rate is 4.55%, that the expected rate of inflation is 2.0%, and that the first college payment is due at time 6 and the last payment is due at time 9. Jane wants to make 9 annual investments (beginning 1 year from now and ending 9 years from now) such that the savings will cover the cost of college. Her first investment (at 1) will be \$A (in real terms) and subsequent investments will grow (in real terms) by 1% per year.

NEED TO SHOW EXCEL FORMULAS:
1) What is the nominal growth rate in her investment amount?

2) What initial nominal investment, A, will be required, at time 1, if Ms. Wells wishes to exactly cover the college expenses? Show your logic.

3) What is the nominal amount of your last investment, in year 9?

4) What is the real amount invested in year 1 and in year 9?

5) Now assume that she wants to pay off the college over 12 years rather than 9 years. When she had less money than needed to pay for college, she needs to take out a loan at an interest rate of 7.10%. Answer (2) and (3) for this scenario.

#### Solution Preview

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Posting ID: 603402
Category: Business / Finance / The Time Value of Money Wrong category? Edit It Level: Year 2
College Savings
Jane has a child and wishes to begin saving for college expenses. Child will enter college in 6 years. Assume child will spend 4 years in college, that the real (ie: inflation adjusted) annual cost of a college education ...

#### Solution Summary

The solution shows all the steps to compute the annuity using the formula for the present value of growing annuity. It also distinguishes between real and nominal growth, and interest rates.

\$2.19