Question

In: Finance

Graham plans to save $100 each month for the next 20 years so he can purchase...

Graham plans to save $100 each month for the next 20 years so he can purchase a boat. If he earns 10% interest annually with monthly compounding, how much money will he have at the end of 20 years if he starts saving today?

Expert Solution

Monthly interest rate = 0.83333% per month

Time = 12* 20 = 240 months

The future value of annuity due formula is used to calculate the ending value of a series of payments or cash flows where the first payment is received immediately. The first cash flow received immediately is what distinguishes an annuity due from an ordinary annuity.

FV of annuity due = (1 + i) * P [{(1 + i) ^n -1}/i]

Where,

Periodic deposit (P) = $100

Interest rate = 0.0083333

Time (n) = 240

Let's put all the values in the formula to solve for FV of annuity due

FV of annuity due = (1 + 0.0083333) * 100 [{(1 + 0.0083333) ^240- 1}/ 0.0083333]

= (1.0083333) * 100 [{(1.0083333) ^240- 1}/ 0.0083333]

= 100.83333 *[7.32801549339119- 1/ 0.0083333]

= 100.83333 *[6.32801549339119/ 0.0083333]

= 100.83333 * 759.36489666653

= 76569.29

So the amount he will have after 20 years is $76569.29

--------------------------------------------------------------------------------------------------------------------------

Feel free to comment if you need further assistance J

Pls rate this answer if you found it useful.

jeff jeffy answered 2 years ago

Adam plans to save 300,000 for his retirement within next 30 years. He is saving every...

Adam plans to save 300,000 for his retirement within next 30 years. He is saving every month as monthly savings and invest those with 10 percent yield. How much does Adam need to save every month?

You are planning to save for retirement over the next 20 years. To do this, you...

You are planning to save for retirement over the next 20 years. To do this, you will invest $1,100 a month in a stock account and $800 a month in a bond account. The return of the stock account is expected to be 10 percent, and the bond account will pay 6 percent. When you retire, you will combine your money into an account with a return of 8 percent. How much can you withdraw each month from your account...

An investor plans the following investments for the next 20 years: 12.00 years of $10,200.00 per...

An investor plans the following investments for the next 20 years: 12.00 years of $10,200.00 per year, and 8.00 years of $13,825.00 per year. She thinks his investments will earn 6.00% a year for the first 12.00 years, and then earn 11.00% per year for the last 8.00 years. How much would the investor have to set aside today if she wants to fund the entire account?

An investor plans the following investments for the next 20 years: 12.00 years of $10,075.00 per...

An investor plans the following investments for the next 20 years: 12.00 years of $10,075.00 per year, and 8.00 years of $13,775.00 per year. She thinks his investments will earn 4.00% a year for the first 12.00 years, and then earn 11.00% per year for the last 8.00 years. How much would the investor have to set aside today if she wants to fund the entire account?

An investor plans the following investments for the next 20 years: 12.00 years of $10,550.00 per...

An investor plans the following investments for the next 20 years: 12.00 years of $10,550.00 per year, and 8.00 years of $13,950.00 per year. She thinks his investments will earn 5.00% a year for the first 12.00 years, and then earn 11.00% per year for the last 8.00 years. How much would the investor have to set aside today if she wants to fund the entire account? PLEASE ROUND TO 2 DECIMAL PLACES. THANKS IN ADVANCE.

Beginning one month from today, you plan to save $250 each month for the next ten...

Beginning one month from today, you plan to save $250 each month for the next ten years. After that, you plan to increase the amount you set aside each month from $250 to $450, remaining at this level for another ten years. In the next ten years, you plan to save $650 each month. Finally, for the last ten years of your investment program, you plan to save $850 each month. The rate of return on your invested funds is...

Jake will retire next month and will have $619,209 in RegisteredRetirement Savings Plans (RRSP’s). He...

Jake will retire next month and will have $619,209 in Registered Retirement Savings Plans (RRSP’s). He wants a quarterly payment at the beginning of each quarter and expects to earn 10.8%, compounded quarterly in the equity and bond markets as an average. What quarterly amount would he be able to withdraw if his fund is expected to last 20 years?

Mr. Rashid plans to purchase the electronics itemsbased on his budget. So he needs a...

Mr. Rashid plans to purchase the electronics items based on his budget. So he needs a purchase planner which will help to calculate the price of electronics items, he can purchase based on the available amount. If Mr. Rashid enters his budget amount and chooses the numbers of electronic items from the list of available electronic items, the purchase planner will calculate the cost of electronics items based on the number of items selected, the total cost of all the...

You are 20 years old now and you will save $10,000 annually for the next 30...

You are 20 years old now and you will save $10,000 annually for the next 30 years and the interest rate is 9%. How much money you will have when you are 50 years old? A. $1,363,075.39 B. $899,937.73 C. $1,112,577.83 D. $998,181.47 What is the PV of $2,000 to be received in 10 years at an interest rate of 8%? A. $980.25 B. $926.39 C. $783.12 D. $1,000

You will recieve a 20-year annuity of $2,750 every month for the next 20 years (the...

You will recieve a 20-year annuity of $2,750 every month for the next 20 years (the first payment is one month from today, two hundred and fourty payments in total) as well as a $125,000 lump sum to be received 20 years from today. What is the present value of these cash flows you will receive in the future if the appropriate discount rate is 7.25% APR?