Business, 21.08.2020 23:01 loveket143

You are planning to save for retirement over the next 25 years. To do this, you will invest $880 per month in a stock account and $480 per month in a bond account. The return of the stock account is expected to be an APR of 10.8 percent, and the bond account will earn an APR of 6.8 percent. When you retire, you will combine your money into an account with an APR of 7.8 percent. All interest rates are compounded monthly. How much can you withdraw each month from your account assuming a withdrawal period of 20 years

Answers: 2

Show answers

Answers

Answer from: keaton191

$14,143.86 can be withdrawn each month from the account for 20 years.

Explanation:

To determine this, the first step is to use the formula for calculating the future value (FV) of ordinary annuity to calculate the FV of both stock and bond as follows:

Calculation of Future Value of Stock

FVs = M × {[(1 + r)^n - 1] ÷ r} (1)

Where,

FVs = Future value of the amount invested in stock after 25 years =?

M = Monthly investment = $880

r = Monthly interest rate = 10.8% ÷ 12 = 0.9%, or 0.009

n = number of months = 25 years × 12 months = 300

Substituting the values into equation (1), we have:

FVs = $880 × {[(1 + 0.009)^360 - 1] ÷ 0.009}

FVs = $880 × 1,522.3445923122

FVs = $1,339,663.24

Calculation of Future Value of Bond

FVd = M × {[(1 + r)^n - 1] ÷ r} (1)

Where,

FVd = Future value of the amount invested in bond after 25 years =?

M = Monthly investment = $480

r = Monthly interest rate = 6.8% ÷ 12 = 0.566666666666667%, or 0.00566666666666667

n = number of months = 25 years × 12 months = 300

Substituting the values into equation (1), we have:

FVd = $480 × {[(1 + 0.00566666666666667)^300 - 1] ÷ 0.00566666666666667}

FVd = $480 × 784.895879465925

FVd = $376,750.02

Calculation of the amount that can be withdrawn monthly for 20 years

To calculate this, the formula for calculating the present value of an ordinary annuity is used as follows:

PV = P × [{1 - [1 ÷ (1+r)]^n} ÷ r] …………………………………. (3)

Where;

PV = Combined present values of stock and bond investments after retirement = FVs + FVb = $1,339,663.24 + $376,750.02 = $1,716,413.26

P = Monthly withdrawal = ?

r = Monthly interest rate = 7.8% ÷ 12 = 0.65%, or 0.0065

n = number of months = 20 years * 12 months = 240

Substitute the values into equation (3) and solve for P to have:

PV = P × [{1 - [1 ÷ (1+r)]^n} ÷ r]

$1,716,413.26 = P × [{1 - [1 ÷ (1 + 0.0065)]^240} ÷ 0.0065]

$1,716,413.26 = P × 121.353915567094

P = $1,716,413.26 / 121.353915567094

P = $14,143.86

Therefore, $14,143.86 can be withdrawn each month from the account for 20 years.

Answer from: Quest

answer; i believe a ( newsletter ) should be sent;

Answer from: Quest

the third answer is correct.

Another question on Business

Business, 22.06.2019 07:40

Xyz corporation has provided the following data concerning manufacturing overhead for july: actual manufacturing overhead incurred $ 69,000 manufacturing overhead applied to work in process $ 79,000 the company's cost of goods sold was $243,000 prior to closing out its manufacturing overhead account. the company closes out its manufacturing overhead account to cost of goods sold. which of the following statements is true? multiple choice manufacturing overhead was overapplied by $10,000; cost of goods sold after closing out the manufacturing overhead account is $253,000 manufacturing overhead was underapplied by $10,000; cost of goods sold after closing out the manufacturing overhead account is $233,000 manufacturing overhead was underapplied by $10,000; cost of goods sold after closing out the manufacturing overhead account is $253,000 manufacturing overhead was overapplied by $10,000; cost of goods sold after closing out the manufacturing overhead account is $233,000

Answers: 1

Answer

Business, 22.06.2019 08:30

In risk management, what does risk control include? a. risk identification b. risk analysis c. risk prioritization d. risk management planning e. risk elimination need this answer now : (

Answers: 3

Answer

Business, 22.06.2019 19:00

12. to produce a textured purée, you would use a/an a. food processor. b. wide-mesh sieve. c. immersion blender d. food mill.

Answers: 1

Answer

Business, 22.06.2019 19:50

The new york company produces high quality chairs. variable manufacturing overhead is applied at a standard rate of $12 per machine hour. each chair requires a standard quantity of six machine hours. production for the month totaled 4,000 units. calculate: the standard cost per unit for variable overhead. select one: a. $130,000 b. $192,000 c. $90,000 d. $100,000

Answers: 2

Answer

You know the right answer?

You are planning to save for retirement over the next 25 years. To do this, you will invest $880 per...

Questions