Explanation Given Information: $1,000 is to be funded for 15 years at 5% per year, in the annuity account. There is to be $20,000 left in the account after 15 years. Formula used: The present value of an investment with future value FV is given by, P V = F V ( 1 + i ) n or P V = F V ( 1 + r m ) m t Present value: If an account with an interest rate of i per compounding period receives a payment of PMT at the end of the compounding period, and the account is down to zero after n periods, then the starting balance of the account is given by, P V = P M T 1 − ( 1 + i ) − n i Calculations: Consider the provided information. As the amount funded is $1,000. Hence, P M T = 1 , 000 . The amount are funded for a period of 15 years. In order to convert it into months, multiply by 12, n = 15 × 12 = 180 And, the interest rate is 5 % per year. Thus, i is given by, 5 % = 5 100 = 0.05 As there are 12 periods. So the interest per period is, i = 0.05 12 Also, the future value of the account is to be $20,000. Thus, F V = 20 , 000 . Since, both the future value and the payments need to be fund. So, the present value is the sum of the two

7th Edition

ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 2.3, Problem 18E

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To calculate: The present value of the annuity account necessary to fund $1,000 per quarter for 15 years, if the account earns 5% per year, if there is to be $20,000 left in the account after 15 years.

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Chapter 2.3, Problem 17E

Chapter 2.3, Problem 19E

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The present value of the annuity account necessary to fund $1,000 per quarter for 15 years, if the account earns 5% per year, if there is to be $20,000 left in the account after 15 years.

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To calculate: The present value of the annuity account necessary to fund $1,000 per quarter for 15 years, if the account earns 5% per year, if there is to be $20,000 left in the account after 15 years.

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