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You are planning for your retirement and have decided the following: you will retire in 35 years...

Question:

You are planning for your retirement and have decided the following: you will retire in 35 years and will make monthly deposits into your retirement account of $400 for the next 15 years and then monthly deposits of $800 for the remaining 20 years until retirement. You have access to an account that earns a 7% rate of return.

a) How much will you have when you retire?

b) Once you retire, you plan to live off of the interest. If you make annual withdrawals, what will be your retirement income?

c) If your goal is to be able to live off of $80,000 per year during retirement (instead of your answer to b), how much more would you have to have at retirement to reach this goal?

Annuity:

An annuity is a long-term financial investment and is intended to assist with shielding you from the risk of outliving your income. Through annuity, your buy installments are changed into regular interval payments that can keep going.

Answer and Explanation: 1

Retirement Age is after 35 years,


For 1st amount after 15 years:


{eq}\begin{align*} &= \$ 400 \times 12 \times 15\\ &= \$ 72,000 \end{align*} {/eq}


Interest on amount:


{eq}\begin{align*} &= \$ 72,000 \times \dfrac{7}{{100}}\\ &= \$ 5,040 \end{align*} {/eq}


Total Amount after 15 years:


{eq}\begin{align*} &= \$ 72,000 + \$ 5,040\\ &= \$ 77,040 \end{align*} {/eq}


For 2nd amount after 20 years:


{eq}\begin{align*} &= \$ 800 \times 12 \times 20\\ &= \$ 192,000 \end{align*} {/eq}


Interest on Amount:


{eq}\begin{align*} &= \$ 192,000 \times \dfrac{7}{{100}}\\ &= \$ 13,440 \end{align*} {/eq}


Total Amount after 20 years:


{eq}\begin{align*} &= \$ 192,000 + \$ 13,440\\ &= \$ 205,440 \end{align*} {/eq}


A) {eq}\begin{align*} {\rm\text{Retirement Amount}} &= \$ 77,040 + \$ 205,440\\ &= \$ 282,480 \end{align*} {/eq}


B) {eq}\begin{align*} {\rm\text{The interest of }}{{\rm\text{1}}^{{\rm\text{st}}}}{\rm\text{and }}{{\rm\text{2}}^{{\rm\text{nd}}}}{\rm\text{one}} &= \$ 5,040 + \$ 13,440\\ &= \$ 18,480 \end{align*} {/eq}


{eq}\begin{align*} {\rm\text{Total Income }} &= \$ 282,480 + \$ 18,480\\ &= \$ 300,960 \end{align*} {/eq}


C) If, the amount is $80,000


{eq}\begin{align*} &= \$ 282,480 + \$ 80,000\\ &= \$ 362,480 \end{align*} {/eq}


Learn more about this topic:

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How to Find the Value of an Annuity

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Chapter 21 / Lesson 15
9.4K

An annuity is a type of savings account that pays back the investor in the future. Learn the formula used to calculate an annuity's value, and understand the importance of labeling specific numbers to calculate an output over time.


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