5-8 ### Financial Formula Identification and Application#### Scenario Analysis:Ten months ago, Marie started making $200 monthly car payments. Based on a 6% annual rate of interest (compounded monthly), what is the value of Marie’s payments today?To identify the conditions, we must first understand the variables involved:- Routine deposits/withdrawals: $200 monthly payments.- Interest rate: 6% annually, compounded monthly.### Equations:1. $ A = P(1 + i)^n $ 2. $ P = \frac{A}{{(1 + i)^n}} $ 3. $ A = P(1 + i)^n $ 4. $ P = \frac{A}{{(1 + i)^n}} $ 5. $ A = R \left( \frac{{(1 + i)^n - 1}}{i} \right) $ 6. $ R = \frac{Ai}{{(1 + i)^n - 1}} $ 7. $ A = R \left( \frac{1 - (1 + i)^{-n}}{i} \right) $ 8. $ R = \frac{Ai}{1 - (1 + i)^{-n}} $### Matching Formulas to Conditions:- **Formula 5**: $ A = R \left( \frac{{(1 + i)^n - 1}}{i} \right) $- **Formula 6**: $ R = \frac{Ai}{{(1 + i)^n - 1}} $- **Formula 7**: $ A = R \left( \frac{1 - (1 + i)^{-n}}{i} \right) $- **Formula 8**: $ R = \frac{Ai}{1 - (1 + i)^{-n}} $### Condition Options:A. Routine deposit/withdrawal is known Interest added periodically Determine future value B. Present value is known Interest added periodically Determine routine deposit/withdrawal C. Future value is known One-time deposit/withdrawal Interest added once Determine present value D. Present value is known One-time deposit/withdrawal Interest added periodically Determine future value E. Present value ### Financial Mathematics Practice Problems#### Problem 1:Starting one month after retiring, Julie plans to withdraw $2000 monthly from her IRA for the next 20 years. Interest in the amount of 1% of the remaining balance is added monthly to the account. How much should Julie have in her account upon retiring?**Formula** = _____ **i** = __________ **n** = ________ **Amt.** = ____________---#### Problem 2:A year after a subdivision was built (built in 1995), a constant number of people started moving in per year. Births started occurring after one year of residency. The number of births each year was the product of the current population and a 5% annual birth rate. People moved in and births occurred on the same day each year. The population in 2000 was 100; how many people moved in each year?**Formula** = _____ **i** = __________ **n** = ________ **Amt.** = ____________---#### Problem 3:For 20 years, Bear deposited monthly into a mutual fund that yielded a 12% annual rate of interest (compounded monthly). A one-time deposit of $200,000 (deposited 20 years ago) has the same result. Based on a 12% annual rate of interest compounded monthly, how much was deposited monthly?**Formula** = _____ **i** = __________ **n** = ________ **Amt.** = ____________---#### Problem 4:Ten months ago, Marie started making $200 monthly car payments. Based on a 6% annual rate of interest (compounded monthly), what is the value of Marie's payments today?**Formula** = _____ **i** = __________ **n** = ________ **Amt.** = ____________---#### Problem 5:Jay has $1,000,000 in his IRA one month before taking his first monthly withdrawal. Interest in the amount of 1% of the remaining balance is added monthly to the account. How much can Jay withdraw monthly, resulting in a zero balance at the end of 20 years?**Formula** = _____ **i** = __________ **n** = ________ **Amt.** = ____________---#### Formulas and Model Breakdown1. **Basic Compound Interest:** \( A = P(1 + in) \

Future value (FV) is crucial to investors and financial planners because they use it to predict how…

1. A = P(1 + in) 2. P= 3. A=P(1+i)n 4. P= 5. A=R[(1+i)n-1] Ai 6. R= (1+i)n-1 A (1 + in) A (1+i)n 7. A =R [1-(1+i)n] 8. R= Ai 1-(1+i)n Match the formulas to the conditions below: Formula 5: A: Routine deposit/withdrawal is known Interest added periodically Determine future value Formula 6: B: Present value is known Interest added periodically Determine routine deposit/withdrawal C: Future value is known One time deposit/withdrawal Interest added once Determine present value D: Present value is known One time deposit/withdrawal Interest added periodically Determine future value Formula 7: Formula 8: E. Present value is known One time deposit/withdrawal Interest added once Determine future value F: Future value is known Interest added periodically Determine routine deposit/withdrawal G: Routine deposit/withdrawal is known Interest added periodically Determine present value H: Future value is known One time deposit/withdrawal Interest added periodically Determine present value

1. A = P(1 + in) 2. P= 3. A=P(1+i)n 4. P= 5. A=R[(1+i)n-1] Ai 6. R= (1+i)n-1 A (1 + in) A (1+i)n 7. A =R [1-(1+i)n] 8. R= Ai 1-(1+i)n Match the formulas to the conditions below: Formula 5: A: Routine deposit/withdrawal is known Interest added periodically Determine future value Formula 6: B: Present value is known Interest added periodically Determine routine deposit/withdrawal C: Future value is known One time deposit/withdrawal Interest added once Determine present value D: Present value is known One time deposit/withdrawal Interest added periodically Determine future value Formula 7: Formula 8: E. Present value is known One time deposit/withdrawal Interest added once Determine future value F: Future value is known Interest added periodically Determine routine deposit/withdrawal G: Routine deposit/withdrawal is known Interest added periodically Determine present value H: Future value is known One time deposit/withdrawal Interest added periodically Determine present value

PFIN (with PFIN Online, 1 term (6 months) Printed Access Card) (New, Engaging Titles from 4LTR Press)

6th Edition

ISBN:9781337117005

Author:Randall Billingsley, Lawrence J. Gitman, Michael D. Joehnk

Publisher:Randall Billingsley, Lawrence J. Gitman, Michael D. Joehnk

Chapter14: Planning For Retirement

Section: Chapter Questions

Problem 2FPE

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