# Joseph will start school on 9/1/14. He is expected to attend school for four years and will need...

## Question:

Joseph will start school on 9/1/14. He is expected to attend school for four years and will need to pay tuition of $50,000 on September 1st of each year. His uncle wants to make an investment on 9/1/10 that will provide sufficient funds for four years of tuition. Assuming he can earn 5% annually, how much must invest on 9/1/10.

A. $27,282

B. $37,976

C. $104,167

D. $200,000

E. $153,156

## Annuity Due:

An annuity due is a fixed-income security that its payments will occur at the beginning of each period. The annuity payment might be either constant or growing, which depends on the initial annuity policies.

## Answer and Explanation: 1

The answer is **E. $153,156**

**Given information: **

- Annual payment = $50,000
- N2 = 4
- N1 = 4
- I = 5%

**Determine the initial deposit: **

{eq}Initial\:deposit = \displaystyle PMT\times\frac{1-(1 + I)^{-N2}}{I}\times (1 + I)\times\frac{1}{(1 + I)^{N1}} {/eq}

{eq}Initial\:deposit = \displaystyle $50,000\times\frac{1-(1 + 5\%)^{-4}}{5\%}\times (1 + 5\%)\times\frac{1}{(1 + 5\%)^{4}} {/eq}

{eq}Initial\:deposit = $153,156 {/eq}

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Chapter 2 / Lesson 7An 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.