Suppose you and your husband have decided that when you retire in 15 years you want...

Suppose you and your husband have decided that when you retire in 15 years you want to take a trip around the world for a year. You realize that you need to begin saving now for this trip of a lifetime. You want to be able to deposit annually (end of year payments) a fixed amount in an interest bearing account. It is estimated that monthly after that you will need to withdraw $5000 monthly for spending money. You will make the down payment at year 15 and the monthly payments will begin the first month after year 15 and will go for 12 months. How much must you deposit annually to be able to pay for these expenses. Assume 6% interest annual rate with monthly compounding.

Solutions

Expert Solution

First we will Calculate the downpayment needed at year 15

Monthly withdrawls after year 15 = $5000, Annual interest rate = 6% with monthly compounding

Monthly rate = Annual interest rate with monthly compounding / 12 = 6% / 12 = 0.50%

No of withdrawls or months = 12

Here Monthly withdrawls form an ordinary annuity. Downpayment at year 15 will equal to present value of monthly withdrawls for 12 months.

We can find the present value of monthly withdrawls or downpayment at year 15 using PV function in excel

Formula to be used in excel: =PV(rate,nper,-pmt)

Using PV function in excel, we get Downpayment at year 15 = $58094.6603

Now we will calculate the amount(end of year) needed to deposit per year

Since the interest rate is compounded monthly, annual deposits will earn interest at effective annual rate

Effective annual rate = (1+ monthly rate)¹² - 1 =(1+0.50%)¹² - 1 = 1.061677 - 1 = 0.061677 = 6.1677%

We can find the amount needed to deposit each year using PMT function in excel

Formula to be used in excel: =PMT(rate,nper,pv,-fv)

In the formula pv = 0 as there is no initial lumpsum deposit

Using PMT function in excel, we get Annual deposit at end of year = 2464.3855 = 2464.39 (rounded to two decimal places)

Amount to be deposited annually to pay for expenses = $2464.39

jeff jeffy answered 2 hours ago

Next > < Previous

Related Solutions

You have decided that you want to be a millionaire when you retire in 44 years....

You have decided that you want to be a millionaire when you retire in 44 years. 1. .If you can earn an annual return of 11.22 percent, how much do you have to invest today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) 2. .What if you can earn an annual return of 5.61 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) 1. amount to...

You’ve decided that you want $1,000,000 in your investment account when you retire 25 years from...

You’ve decided that you want $1,000,000 in your investment account when you retire 25 years from today. If you already have $100,000 in the account, and it earns a nominal rate of 8% per year, compounded quarterly, how much money will you have to deposit into that account per year in order to reach your goal?

Suppose you have determined that you want to have retirement savings of $5,000,000 when you retire...

Suppose you have determined that you want to have retirement savings of $5,000,000 when you retire at age 65, 42 years after you graduate, at age 23. Looking at the long history of the market, you are confident that you can earn at 10% per annum on a well-diversified equity portfolio. Required: a) Calculate much would you have to save annually at the end of each year for the next 42 years to reach your $5,000,000 goal assuming a 10%...

1- ) You want to have $3 million when you retire in 40 years. If you...

1- ) You want to have $3 million when you retire in 40 years. If you can earn 12% per year, how much do you need to deposit on a monthly basis if the first payment is made in one month? 2- ) What if the first payment is made today? 3- ) You are considering ABC’s preferred stock that is expected to pay a quarterly dividend of $1.00 forever. If your desired return is 10% per year, how much...

5. You want to retire in ten years and you currently have no wealth to your...

5. You want to retire in ten years and you currently have no wealth to your name. You estimate that you’ll will need $1.8M at your retirement date in order to live out the remainder of your life comfortably. You plan to make 10 equal annual payments into an account at the end of each year from now until your retire. If you can earn 8%/year, compounded annually, how much must you invest at the end of each year for...

If you want to have an $500,000 amount (F) when you retire in 35 years, what...

If you want to have an $500,000 amount (F) when you retire in 35 years, what equal series amount (A) do you need to invest each year with a 5% interest rate? (Hint, use (A/F, i, n)) Same question as 1, but how much is the equal series amount (A) if you had procrastinated for 10 years and now have only 25 years to accumulate the $500,000 desired at retirement? Same question as 2, but the interest rate is 7%,...

You are 20 years old and you want to retire when you have saves$1 million....

You are 20 years old and you want to retire when you have saves $1 million. You have inherited $250,000 and will not add any other savings to that amount. The money will be conservatively invested at 6% per annum. At what age will you be able to retire a millionaire?

You want to have $1,000,000 when you retire in 30 years. You expect to earn 12%...

You want to have $1,000,000 when you retire in 30 years. You expect to earn 12% compounded monthly over the entire 30-year period. How much extra money per month must you deposit if you choose to fund using an ordinary annuity technique rather than an annuity due technique?

You want to have $3 million in real dollars in an account when you retire in 30 years

You want to have $3 million in real dollars in an account when you retire in 30 years. The nominal return on your investment is 13 percent and the inflation rate is 3.7 percent. What real amount must you deposit each year to achieve your goal? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Deposit amount = _______

You have decide to retire in 20 years and you want to have $2,000,000 e in...

You have decide to retire in 20 years and you want to have $2,000,000 e in the bank when you retire. You currently have $50,000 k. in the bank. The bank pays 4.00% interest compounded yearly. How much money do you need to deposit in your bank account each year in order to meet your retirement goal?

Subjects