Asked by Rebecca Groen on May 09, 2024
Verified
An individual wants to receive end-of-month payments of $1,200 for 20 years after she retires 15 years from now. What lump amount must she invest today to provide the retirement income? Assume the investment earns 7% compounded monthly for the entire 35 years.
A) $49,864.93
B) $54,645.42
C) $54,328.50
D) $187,835.65
E) $155,681.89
Compounded Monthly
Interest calculation method where interest is added to the principal balance monthly, affecting the total interest accrued over time.
Retirement Income
The amount of money or income a person receives after retiring from work, which can come from various sources such as pensions, investments, and savings.
- Use present value methodologies to figure out how much needs to be invested now to meet financial aspirations in the future.
- Achieve insight into the basic principles behind time value of money calculations.
- Analyze the financial implications of various interest rates and investment periods on savings and loan scenarios.
Verified Answer
MG
Marissa GalloMay 14, 2024
Final Answer :
C
Explanation :
To solve this, we use the concept of the time value of money, specifically the present value of an annuity (for the retirement payments) and the present value of a single sum (for the lump sum investment needed today). First, calculate the present value of the annuity that starts 15 years from now and pays $1,200 monthly for 20 years at a 7% annual interest rate compounded monthly. Then, calculate the present value of that amount as of today, accounting for the 15 years until retirement at the same interest rate. The correct answer, after performing these calculations, is $54,328.50.
Learning Objectives
- Use present value methodologies to figure out how much needs to be invested now to meet financial aspirations in the future.
- Achieve insight into the basic principles behind time value of money calculations.
- Analyze the financial implications of various interest rates and investment periods on savings and loan scenarios.