PERSONAL FINANCE (LL)
13th Edition
ISBN: 9781337885942
Author: GARMAN
Publisher: CENGAGE L
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 5, Problem 1DTM
Invest Now or Later? Twins Natalie and Kaitlyn are both age 27. They both live in Warren, Ohio. Beginning at age 27, Natalie invests $2,000 per year for ten years and then never sets aside another penny. Kaitlyn waits ten years and then invests $2,000 per year for the next 30 years. Assuming they both earn 7 percent, how much will each twin have at age 67? (Hint: Use Appendixes A.1 and A.3 or visit the Garman/Forgue companion website.
Expert Solution & Answer
Summary Introduction
To calculate:The future value of the investment of each person.
Introduction: Time value of money is the concept of finance which calculates the effect of time over the value of money. As per this concept the present value of a future amount is lower than the future value. The present value/ future value of an amount is calculated using the interest rate as discount rate.
Answer to Problem 1DTM
The future value of the investment of each person is as follows:
| Future value of investment | |
| N | $ 2,10,350.68 |
| K | $ 7,31,069.92 |
Explanation of Solution
The future value of the investment of each person is calculated as follows:
| N: | |
| Annual investment (A) | $ 2,000 |
| Years of investment (B) | 10 |
| Interest rate (C) | 7% |
| Future value of annuity $1 (7%, 10 years) (D) | 13.8165 |
| Future value after 10 years (E) (A | $ 27,633 |
| Remaining years (F) (67-37) | 30 |
| Future value of lump sum $1 (7%, 30 years) (G) | 7.6123 |
| Future value at the age of 67 (E | $ 2,10,350.68 |
| K: | |
| Annual investment (A) | $ 2,000 |
| Years of investment (B) | 30 |
| Interest rate (C) | 7% |
| Future value of annuity $1 (7%, 30 years) (D) | 94.4608 |
| Future value after 30 years (E) (A | $ 1,88,921.60 |
| Remaining years (F) (67-47) | 20 |
| Future value of lump sum $1 (7%, 20 years) (G) | 3.8697 |
| Future value at the age of 67 (E | $ 7,31,069.92 |
Want to see more full solutions like this?
Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Use the binomial method to determine the value of an American Put option
at time t = 0. The option expires at time t = T = 1/2 and has exercise price
E = 55. The current value of the underlying is S(0) = 50 with the underlying
paying continuous dividends at the rate D = 0.05. The interest rate is r = 0.3.
Use a time step of St = 1/6. Consider the case of p = 1/2 and suppose the
volatility is σ = 0.3. Perform all calculations using a minimum of 4 decimal
places of accuracy.
=
Consider a European chooser option with exercise price E₁ and expiry date
T₁ where the relevant put and call options, which depend on the value of the
same underlying asset S, have the same exercise price E2 and expiry date T₂.
Determine, in terms of other elementary options, the value of the chooser option
for the special case when T₁ = T2. Clearly define all notation that you use.
The continuous conditional probability density function pc(S, t; S', t') for a risk
neutral lognormal random walk is given by
Pc(S, t; S', t') =
1
σS'√2π(t' - t)
-
(log(S/S) (ro²)(t − t)]
exp
202 (t't)
In the binomial method, the value of the underlying is Sm at time step môt
and the value of the underlying at time step (m + 1)St is Sm+1. For this case
evaluate
Ec[(Sm+1)k|Sm] = [°° (S')*pc(S™, mdt; S', (m + 1)8t)dS'
showing all steps, where k is a positive integer with k ≥ 1.
You may assume that
1
e
(x-n)2
2s2dx = 1
for all real numbers n and s with s > 0.
Chapter 5 Solutions
PERSONAL FINANCE (LL)
Ch. 5.1 - Prob. 1CCCh. 5.1 - Explain the circumstances when it would be...Ch. 5.1 - Prob. 3CCCh. 5.1 - Summarize your insurance protections when you have...Ch. 5.2 - Explain why opening a checking account and a money...Ch. 5.2 - Prob. 2CCCh. 5.2 - Prob. 3CCCh. 5.2 - Prob. 4CCCh. 5.3 - Prob. 1CCCh. 5.3 - Prob. 2CC
Ch. 5.4 - Prob. 1CCCh. 5.4 - Prob. 2CCCh. 5.4 - Prob. 3CCCh. 5.4 - Prob. 4CCCh. 5.5 - Prob. 1CCCh. 5.5 - Prob. 2CCCh. 5 - Invest Now or Later? Twins Natalie and Kaitlyn are...Ch. 5 - Prob. 2DTMCh. 5 - Reconciling a Checking Account. Andrew Parker, of...Ch. 5 - Saving for College. You want to create a college...Ch. 5 - Prob. 5DTMCh. 5 - Prob. 1FPCCh. 5 - Prob. 2FPCCh. 5 - Prob. 3FPCCh. 5 - Prob. 4FPCCh. 5 - Prob. 5FPCCh. 5 - Prob. 6FPCCh. 5 - Prob. 7FPCCh. 5 - Prob. 8FPCCh. 5 - Keep Your Accounts Current. Go online every few...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, finance and related others by exploring similar questions and additional content below.Similar questions
- John and Jane Doe, a married couple filing jointly, have provided you with their financial information for the year, including details of federal income tax withheld. They need assistance in preparing their tax return. W-2 Income: John earns $150,000 with $35,000 withheld for federal income tax. Jane earns $85,000 with $15,500 withheld for federal income tax. Interest Income: They received $2500 in interest from a savings account, with no tax withheld. Child Tax Credit: They have two children under the age of 17. Mortgage Interest: Paid $28,000 in mortgage interest on their primary residence. Property Taxes: Paid $4,800 in property taxes on their primary residence. Charitable Donations: Donated $22,000 to qualifying charitable organizations. Other Deductions: They have no other deductions to claim. You will gather the appropriate information and complete the forms provided in Blackboard (1040, Schedule A, and Schedule B in preparation of their tax file.arrow_forwardOn the issue date, you bought a 20-year maturity, 5.85% semi-annual coupon bond. The bond then sold at YTM of 6.25%. Now, 5 years later, the similar bond sells at YTM of 5.25%. If you hold the bond now, what is your realized rate of return for the 5-year holding period?arrow_forwardBond Valuation with Semiannual Payments Renfro Rentals has issued bonds that have an 11% coupon rate, payable semiannually. The bonds mature in 17 years, have a face value of $1,000, and a yield to maturity of 9.5%. What is the price of the bonds? Round your answer to the nearest cent.arrow_forward
- analyze at least three financial banking products from both the liability side (like time deposits, fixed income, stocks, structure products, etc). You will need to examine aspects such as liquidity, risk, and profitability from a company and an individual point of view.arrow_forwardHow a does researcher ensure that consulting recommendations are data-driven? What does make it effective, and sustainable? Please help explain and give the example How does DMAC help researchers to improve their business processes? How to establish feedback loops for ongoing refinement. Please give the examplesarrow_forwardDon't used hand raiting and don't used Ai solutionarrow_forward
- Explain what the business model of payday lenders, title pawn lenders, and “credit approved” used car dealers.arrow_forwardThe current NPV of a $30 million bond with 9% interest, 8% coupon rate, and discounted at $95arrow_forwardCould you please help to explain the DMAIC phases and how a researcher would use them to conduct a consulting project? What is a measure process performance and how to analyze the process? What is an improve process performance and how the control improves process and future process performance?arrow_forward
- Consider the two stocks below. Graph the frontier of combinations of the two stocks. Show the effect on the frontier of varying the correlation from −1 to +1. 1 2 3 Mean A B C D TWO STOCKS Varying the correlation coefficient Stock A Stock B 3.00% 8.00% 4 Sigma 15.00% 22.00% 5 Correlation 0.3000 Farrow_forwardLindsay is 30 years old and has a new job in web development. She wants to make sure that she is financially sound by the age of 55, so she plans to invest the same amount into a retirement account at the end of every year for the next 25 years. (a) Construct a data table in Excel that will show Lindsay the balance of her retirement account for various levels of annual investment and return. If Lindsay invests $10,000 at return of 6%, what would be the balance at the end of the 25th year? Note that because Lindsay invests at the end of the year, there is no interest earned on the contribution for the year in which she contributes. Round your answer to a whole dollar amount. $ (b) Develop a two-way table for annual investment amounts of $5,000 to $20,000 in increments of $1,000 and for returns of 0% to 12% in increments of 1%. From the 2-way table, what are the minimum annual investments Lindsay must contribute for annual rates ranging from 6% to 11%, if she wants to…arrow_forwardDoes Airbnb have any impaired assets? If so, what are they?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Cornerstones of Cost Management (Cornerstones Ser...AccountingISBN:9781305970663Author:Don R. Hansen, Maryanne M. MowenPublisher:Cengage Learning
Cornerstones of Cost Management (Cornerstones Ser...
Accounting
ISBN:9781305970663
Author:Don R. Hansen, Maryanne M. Mowen
Publisher:Cengage Learning
The Economics Of MARRIAGE; Author: Economic Raven;https://www.youtube.com/watch?v=I_M3RIMWju8;License: Standard Youtube License