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You are planning your retirement in 10 years. You currently have $175,000 in a bond account and...

Question:

You are planning your retirement in 10 years. You currently have $175,000 in a bond account and $615,000 in a stock account. You plan to add $6,500 per year at the end of each of the next 10 years to your bond account. The stock account will earn a return of 11.25% and the bond account will earn a return of 7.75%. When you retire, you plan to withdraw an equal amount for each of the next 25 years at the end of each year and have nothing left. Additionally, when you retire you will transfer your money to an account that earns 7%. How much can you withdraw each year in your retirement?

Annuity:

Annuity refers to a series of cash flows which is received or paid periodically. Present value of the annuity is the discounted value of all the cash flows. Future value of annuity refers to the compounded value of all the cash flows at the end of the annuity.

Answer and Explanation: 1

The formulas to be used in the question are:

Future value = Present value x (1 + Rate)^Number of years

Future value of annuity = Annuity x ((1 + Rate)^Number of years - 1) / Rate

Present value of annuity = Annuity x PVAF(r,n)

PVAF or present value annuity factor is the sum of discounting factors at a given rate r for n number of years

It can be calculated using the following formula:

We need to find out the future value of annuity of both the accounts at the time of retirement and then we will use the formula of present value of annuity to find out the withdrawals possible.

Value of the bond account
= Future value of the lumpsum value + Future value of annuity
= 175000 x 1.0775^10 + 6500 x (1.0775^10 - 1) / 0.0775
= $462,208.86

Value of the stock account
= 615000 x 1.1125^10
= $1,785,974.74

Total value at retirement
= 462208.86 + 1785974.74
= $2,248,183.60

Now,

This is the present value of annuity for retirement period.

So,

Annuity
= 2,248,183.60 / PVAF(7%,25 years)
= 2,248,183.60 / 11.6536
= $192,917.52


Learn more about this topic:

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How to Find the Value of an Annuity

from

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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