Jorge inherited an annuity worth $4,335.57 from his uncle. The annuity will pay him seven equal...


Jorge inherited an annuity worth $4,335.57 from his uncle. The annuity will pay him seven equal payments of $950 at the end of each year.

Jorge's friend, Rafael, has hired a financial planner for advice on retirement. Considering Rafael's current expenses and expected future lifestyle changes, the financial planner has stated that once Rafael crosses a threshold of $12,083,115 in savings, he will have enough money for retirement. Rafael has nothing saved for his retirement yet, so he plans to start depositing $55,000 in a retirement fund at a fixed rate of 12.00% at the end of each year. It will take .......................... years for Rafael to reach his retirement goal.

Time Value of Money:

An annuity investment requires one to save an equal deposit each period. To analyze the annuity investment we apply the time value of money (TVM) theory which holds that a dollar invested today will grow in value over time and have a higher worth in the future because it earns interest. Depositing money in a savings account for retirement applies this principle. TVM theory is constructed on four elements, present value, future value, number of periods, and interest rate. If we are provided with the other three variables, we can derive the number of periods using the method of logarithms.

Answer and Explanation: 1

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Future Value = $12,083,115

Annuity = $55,000

r =12.00%

{eq}\begin{align*} \ FV _{OA} & = Annuity * \dfrac{(1+ r ) ^{n} - 1}{ r}\\ 12,083,115 &...

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Present and Future Value: Calculating the Time Value of Money


Chapter 11 / Lesson 2

Study the time value of money formula. Learn the time value of money definition and practice how to calculate time value of money to understand the relation to purchasing power.

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