A couple has decided to start a college educational trust fund for their new born child. Suppose...

Question:

A couple has decided to start a college educational trust fund for their new born child. Suppose a couple made a deposited an initial $1,000 into the account on the child's actual day of birth and then on each subsequent birthdays, they made a deposited $5,000 into the account for the first 10 years. After the tenth year, the couple stopped depositing money into the account. When the child goes off to college, the trust fund will pay her R dollars on her 18^th, 19^th, 20^th, 21^st, and 22^nd birthday.

Use the TVM solver to help determine the value of R if the money earns 2.15% interest compounded annually. Show in detail how you arrived at your answer. Your final answer should be in the form of a sentence. Write short comments in your solution that describe the steps that you use to solve this problem.

Time Value Of Money:

The concept of the time value of money is an important extend in the finance industry. This concept describes that the value of a dollar in 10 years will be different from the value of a dollar today. Commonly, the value of money will drop down due to the inflation, which will reduce the purchasing power of money over years.

Answer and Explanation: 1

Given information:

  • Investment type: Trust fund
  • Initial deposit (CF0) = $1,000
  • CF1 = CF2 = ... = CF10 = $5,000
  • N1 = 10
  • N2 = 8
  • Annual payment = R
  • N3 = 5
  • I = 2.15%

In this case, the trust fund should be considered as an annuity that has both the accumulation and distribution phase. To determine the value of R, the value of the trust fund at year 18th should be computed, which is the future value of all deposits.

Estimate the value of the trust fund at the 10th birthday:

{eq}Value_{10} = \displaystyle CF0\times (1 + I)^{N1} + CF1\times\frac{(1 + I)^{N1}-1}{I}\times (1 + I) {/eq}

{eq}Value_{10} = \displaystyle $1,000\times (1 + 2.15\%)^{10} + \$5,000\times\frac{(1 + 2.15\%)^{10}-1}{2.15\%}\times (1 + 2.15\%) {/eq}

{eq}Value_{10} = $57,547.80 {/eq}

Estimate the value of the trust fund at the 18th birthday:

{eq}Value_{18} = \displaystyle Value_{10}\times (1 + I)^{N2} {/eq}

{eq}Value_{18} = \displaystyle \$57,547.80\times (1 + 2.15\%)^{8} {/eq}

{eq}Value_{18} = $68,223.77 {/eq}

Estimate the value of R:

{eq}Value_{18} = \displaystyle R\times\frac{1-(1 + I)^{-N3}}{I} \times (1 + I) {/eq}

{eq}$68,223.77 = \displaystyle R\times\frac{1-(1 + 2.15\%)^{-5}}{2.15\%} \times (1 + 2.15\%) {/eq}

{eq}R = $14,231.35 {/eq}


Learn more about this topic:

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What is Annuity? - Definition & Formula

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Chapter 2 / Lesson 7
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An annuity is a fixed amount of income paid at regular intervals, such as monthly or quarterly. Learn the definition and formula for annuity, review examples of annuities, and understand how to determine the value of annuities.


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