Question

In: Finance

You would like to have $650,000 when you retire in 40 years. How much should you...

You would like to have $650,000 when you retire in 40 years. How much should you invest each quarter if you can earn a rate of 2.7% compounded quarterly?

a) How much should you deposit each quarter?

b) How much total money will you put into the account?

c) How much total interest will you earn?

Expert Solution

(a) Here, the deposits will be same every quarter, so it is an annuity. The future value of annuity is $650000. Here we will use the future value of annuity formula as per below:

FVA = P * ((1 + r)ⁿ - 1 / r)

where, FVA is future value of annuity = $650000, P is the periodical amount, r is the rate of interest = 2.7% compounded quarterly. So quarterly rate = 2.7% / 4 = 0.675% and n is the time period = 40 * 4 = 160 quarters.

Now, putting these values in the above formula, we get,

$650000 = P * ((1 + 0.675%)¹⁶⁰- 1 / 0.675%)

$650000 = P * ((1 + 0.00675)¹⁶⁰ - 1 / 0.00675)

$650000 = P * ((1.00675)¹⁶⁰- 1 / 0.00675)

$650000 = P * (2.93401361434 - 1/ 0.00675)

$650000 = P * (1.93401361434 / 0.00675)

$650000 = P * 286.520535458

P = $650000 / 286.520535458

P = $2268.60

So, the amount of money that we need to deposit each quarter is $2268.60.

(b) Total money that will be put into account = $2268.60 * 160 = $362976

(c) Total interest = Future value - Total money invested

Total interest = $650000 - $362976 = $287024

jeff jeffy answered 6 months ago

You would like to have $600,000 when you retire in 30 years. How much should you...

You would like to have $600,000 when you retire in 30 years. How much should you invest each quarter if you can earn a rate of 3% compounded quarterly? a) How much should you deposit each quarter? $ b) How much total money will you put into the account? $ c) How much total interest will you earn?

11.You want to be a millionaire when you retire in 40 years. a. How much do...

11.You want to be a millionaire when you retire in 40 years. a. How much do you have to save each month if you can earn an annual return of 9.7 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. How much do you have to save each month if you wait 10 years before you begin your deposits? (Do not round intermediate calculations and round your answer to 2 decimal places,...

You hope to retire in 30 years, when you do, you would like to have the...

You hope to retire in 30 years, when you do, you would like to have the purchasing power of $100,000 today, during each year of retirement. Your cash is needed at the beginning of each year of retirement. Inflation is expected to be 3% per year from now until the end of your retirement. Your retirement will last 25 years, you expect your 401k to earn 5% per year during your retirement years. How much money do you need at...

Given the following information: You are 40 years old and you would like to retire at...

Given the following information: You are 40 years old and you would like to retire at age 70 (assume social security benefits at that age will be $3,000 per month). You do not have a defined benefit plan; you are just starting to invest in a 401k , current savings are zero (you recently bought a home). You estimate your life span to 90 yrs of age, and you need annual retirement income of 100,000 per year (use todays dollars)...

You’d like to buy a small ranch when you retire in 40 years. You estimate that...

You’d like to buy a small ranch when you retire in 40 years. You estimate that in 40 years you’ll need $7 million to do so. If your savings can earn 1.1% per month, how much will you need to save each month (for 40 years), starting next month, in order to reach your goal? Round to the nearest cent. [Hint: Note that the question gives us the monthly interest rate. This is the periodic rate, which is i/m in...

You would like to retire in 40 years with $1,000,000. Assume you could earn 6% on...

You would like to retire in 40 years with $1,000,000. Assume you could earn 6% on your investment. How much would you have to save each month? (Assume end-of period payments).

you will work for 40 years then you will retire. when yiu retire, you will make...

you will work for 40 years then you will retire. when yiu retire, you will make the first of 40 annual investments of $7549 in a fund. the fund is expected to return 9.9% per year, how much will you have on the day that you make your last deposit?

You are now 25 years old. You would like to retire when you are 65 years old.

You are now 25 years old. You would like to retire when you are 65 years old. You want to receive starting at 65 an annual income of $150,000 per year until you are 95. How much money must you have in your retirement account when you are 65? Assume you can earn 4% per annum.

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...

If you want to be a millionaire when you retire in 50 years, how much must...

If you want to be a millionaire when you retire in 50 years, how much must you save each month if you can earn a 6% annual rate of return? what is the effective annual interest rate on the imvestment? please use formula and show work