Concept explainers
To determine: The amount to be saved from 11 to 30 years in each month.
Annuity refers to the payments of equal amount to be made after certain periods. These payments are made monthly, semi-annually or annually.
Effective Annual Rate:
The effective annual rate is the rate, which is incurred or received on various investment or loans. The effective annual rate is affected by the increase in compounding years.
Explanation of Solution
Solution:
Given,
The time period will be 240 months
The effective annual rate before retirement is 8%.
The effective annual rate after retirement is 11%.
Calculation of the value of the monthly savings after 11th year till 30th year:
The formula to calculate the monthly savings is,
Substitute $2,021,528 for
The monthly savings are $2,499.
Working note:
Calculation of the annual percentage rate before retirement:
The annual percentage rate is 10.48%.
Calculation of the annual percentage rate after retirement:
The annual percentage rate is 7.72%.
Calculation of the monthly interest rate before retirement:
The monthly interest rate before retirement is 0.873%.
Calculation of the monthly interest rate after retirement:
The monthly interest rate before retirement is 0.643%.
Calculation of the future value after monthly savings of ten years:
The future value is $442,130.
Calculation of the remaining amount of future value:
The amount remaining after the purchase of cabin is $92,130.
Calculation of the future value of the remaining amount after the repurchase of the cabin:
The future value is $742,752.
Calculation of the value of
The annuity after 30 years is $2,441,780.
Calculation of the value of inheritance after 30 years:
The annuity after 30 years is $322,500.
Calculation of the total required funds at requirement:
The total funds required are $2,021,528.
Thus, the amount to be saved from 11 years to 30 years each month is $2,499.
Want to see more full solutions like this?
Chapter 4 Solutions
Corporate Finance (The Mcgraw-hill/Irwin Series in Finance Insurance and Real Estate)
- Funding a retirement goal. Austin Miller wishes to have 800,000 in a retirement fund 20 years from now. He can create the retirement fund by making a single lump-sum deposit today. a. If upon retirement in 20 years, Austin plans to invest 800,000 in a fund that earns 4 percent, what is the maximum annual withdrawal he can make over the following 15 years? b. How much would Austin need to have on deposit at retirement in order to withdraw 35,000 annually over the 15 years if the retirement fund earns 4 percent? c. To achieve his annual withdrawal goal of 35,000 calculated in part b, how much more than the amount calculated in part a must Austin deposit today in an investment earning 4 percent annual interest?arrow_forwardIf you are saving the same amount each month in order to buy a new sports car when the new models are released, which of the following will help you determine the savings needed? A. future value of one dollar ($1) B. present value of one dollar ($1) C. future value of an ordinary annuity D. present value of an ordinary annuityarrow_forwardCalculating interest earned and future value of savings account. If you put 6,000 in a savings account that pays interest at the rate of 3 percent, compounded annually, how much will you have in five years? (Hint: Use the future value formula.) How much interest will you earn during the five years? If you put 6,000 each year into a savings account that pays interest at the rate of 4 percent a year, how much would you have after five years?arrow_forward
- EBK CONTEMPORARY FINANCIAL MANAGEMENTFinanceISBN:9781337514835Author:MOYERPublisher:CENGAGE LEARNING - CONSIGNMENTPfin (with Mindtap, 1 Term Printed Access Card) (...FinanceISBN:9780357033609Author:Randall Billingsley, Lawrence J. Gitman, Michael D. JoehnkPublisher:Cengage LearningPFIN (with PFIN Online, 1 term (6 months) Printed...FinanceISBN:9781337117005Author:Randall Billingsley, Lawrence J. Gitman, Michael D. JoehnkPublisher:Cengage Learning
- Cornerstones of Financial AccountingAccountingISBN:9781337690881Author:Jay Rich, Jeff JonesPublisher:Cengage LearningFinancial Accounting: The Impact on Decision Make...AccountingISBN:9781305654174Author:Gary A. Porter, Curtis L. NortonPublisher:Cengage Learning