Explanation Given Information: An investment with compound amount $ 100 , 000 made for 50 years at 5 % interest compounded annually. Formula used: Compounding period can be defined as the duration or length of time from one interest payment to the next. If an investment made for 4 years at 6 % compounded annually (once per year) then it would have four compounding period which can be calculated by formula given below: Compounding periods = Term of investments ( years ) × m Here, m is the period per year. The interest rate per period can be calculated by dividing the annual, or nominal, rate by the number of periods per year, Interest rate per period = Nominal rate Period per year The present value (principal) can be calculated by the formula given below: Principal = Table factor × Compound amount In present value table 11-2, the table factor is the intersection of the rate-per-period column and the number-of-periods row is the present value of $ 1 at compound interest. When the number of periods of an investment is greater than the number of periods provided by the present value table, then compute a new table factor by following below steps: Step 1. For the defined interest rate per period, evaluate the two table factors that represent half, or values as close as possible to half, of the periods required. Step 2. Multiply the two table factors from step 1 to form the new factor. Step 3. Round the new factor to five decimal places. Calculation: Consider the compound amount $ 100 , 000 made for 50 years at 5 % interest compounded annually and solve as shown below: Since, the variables-compound amount, time period (years), nominal rate and interest compounded are given; therefore, the compounding period can be calculated as below: Compounding period = Years × Period per year = 50 × 1 = 50 Calculate the interest rate per period

Contemporary Mathematics for Business & Consumers

8th Edition

ISBN: 9781305585447

Author: Robert Brechner, Geroge Bergeman

Publisher: Cengage Learning

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Chapter 11, Problem 14AT

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To calculate: The new table factor and the present value (principal) that has compound amount $100,000 made for 50 years at 5% interest compounded annually.

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Chapter 11, Problem 13AT

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Chapter 11 Solutions

Contemporary Mathematics for Business & Consumers

Ch. 11.I - Gail Parker invested $10,000 at 6% interest...Ch. 11.I - Jenny Chao invested $20,000 at 6% interest...Ch. 11.I - Prob. 3TIE Ch. 11.I - Jill Quinn invested $7,000 in a certificate of...Ch. 11.I - Prob. 5TIE Ch. 11.I - Prob. 1RE Ch. 11.I - For the following investments, find the total...Ch. 11.I - For the following investments, find the total...Ch. 11.I - Prob. 4RE Ch. 11.I - Prob. 5RE

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The new table factor and the present value (principal) that has compound amount $ 100 , 000 made for 50 years at 5 % interest compounded annually.

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To calculate: The new table factor and the present value (principal) that has compound amount $100,000 made for 50 years at 5% interest compounded annually.

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Chapter 11 Solutions