# On January 1, 2011, Shannon Company completed the following transactions (assume a 10 percent...

## Question:

On January 1, 2011, Shannon Company completed the following transactions (assume a {eq}10 {/eq} percent annual interest rate):

a. Bought a delivery truck and agreed to pay {eq}\$50,000 {/eq} at the end of three years. b. Rented an office building and was given the option of paying {eq}\$10,000 {/eq} at the end of each of the next three years or paying {eq}\$28,000 {/eq} immediately. c. Established a savings account by depositing a single amount that will increase to {eq}\$40,000 {/eq} at the end of seven years.

d. Decided to deposit a single sum in the bank that will provide {eq}10 {/eq} equal annual year-end payments of {eq}\$15,000 {/eq} to a retired employee (payments starting December 31, 2011). 1. In (a), what is the cost of the truck that should be recorded at the time of purchase? 2. In (b), which option for the office building should the company select? 3. In (c), what single amount must be deposited in this account on January 1, 2011? 4. In (d), what single sum must be deposited in the bank on January 1, 2011? ## Time value of money Time value of money basically means that the worth of$1 today will increase with time depending upon the prevailing interest rates in the market such that if the rate is 10% value of such dollar after a year would be 1.1. ## Answer and Explanation: 1 1. {eq}\begin{align*} \text{Purchase cost}&= \text{Future value}\times \text{PV}_{( n = 3, \: i = 10\%)}\\ &= \50,000 \times 0.75131\\ &= \37,565 \end{align*} {/eq} 2. {eq}\begin{align*} \text{Present value}&= \text{Annuity amount}\times \text{PVA}_{( n = 3, \: i = 10\%)}\\ &= \10,000 \times 2.48685\\ &= \24,868 \end{align*} {/eq} The company must choose to pay10,000 at the end of each of the next three years as the present value of annuity is less than paying 28,000 immediately. 3. {eq}\begin{align*} \text{Amount to deposit}&= \text{Single amount}\times \text{PV}_{( n = 7, \: i = 10\%)}\\ &= \40,000 \times 0.51316\\ &= \20,526 \end{align*} {/eq} 4. {eq}\begin{align*} \text{Amount to deposit}&= \text{Single amount}\times \text{PVA}_{( n = 10, \: i = 10\%)}\\ &= \15,000 \times 6.14457\\ &= \\$92,168 \end{align*} {/eq}

How to Calculate the Present Value of an Annuity

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Chapter 8 / Lesson 3
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Learn how to find present value of annuity using the formula and see its derivation. Study its examples and see a difference between Ordinary Annuity and Annuity Due.