Explanation Given Information: An investment with principal $ 21 , 800 invested at 2.9 % interest compounded semi-annually for 6 years. 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 Compound interest formula: Compound amount ( A ) can be calculated as, Compound amount ( A ) = P ( 1 + i ) n Here, the principal ( P ) , Interest rate per period ( i ) and the number of compounding periods ( n ) are known. Compound Interest: It can be calculated by subtracting the principal from compound amount. Compound Interest = Compound Amount − Principal Steps for solving the compound interest formula: Step I: Add 1 to the interest rate per period i . Step II: raise to the n th power to the resultant step 1 by using the y x key on your calculator. Step III: Multiply the resultant of step 2 by the compound amount P . Calculation: Consider principal $ 21 , 800 invested at 2.9 % interest compounded semi-annually for 6 years and solve as 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: Substitute the values in the formula for interest rate per period and simplify, Interest rate per period = Nominal rate Period per year = 2

Contemporary Mathematics for Business & Consumers

8th Edition

ISBN: 9781305585447

Author: Robert Brechner, Geroge Bergeman

Publisher: Cengage Learning

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Chapter 11, Problem 29AT

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To calculate: The compound amount and the compound interest for an investment with principal $21,800 invested at 2.9% interest compounded semi-annually for 6 years.

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Chapter 11, Problem 28AT

Chapter 11, Problem 30AT

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In this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0 given (under the measure P) by d.St 0.03 St dt + 0.2 St dwt, with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to price an option on this stock (which we name cubic put). This option is European-type, with maturity 3 months (i.e. T = 0.25 years), and payoff given by F = (8-5)+ (a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure Q. (You don't need to prove it, simply give the answer.) (b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2. (c) Let X = S. Find the Stochastic Differential Equation satisfied by the process (Xt) under the measure Q. (d) Find an explicit expression for X₁ = S3 under measure Q. (e) Using the results above, find the price of the cubic put option mentioned above. (f) Is the price in (e) the same as in question (b)? (Explain why.)

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 compound amount and the compound interest for an investment with principal $ 21 , 800 invested at 2.9 % interest compounded semi-annually for 6 years.

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To calculate: The compound amount and the compound interest for an investment with principal $21,800 invested at 2.9% interest compounded semi-annually for 6 years.

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