Jody's grandparents deposited $1,200 annually to a savings account and increased the deposits at a rate...

Jody's grandparents deposited $1,200 annually to a savings account and increased the deposits at a rate of 3% annually for 5 years. What is the present value of this investment earning 8% annually?

Solutions

Expert Solution

There is a growing annuity.

Given,

First deposit = F = 1,200

Rate = r = 8% = 8/100 = 0.08

Number of year = n = 5

Rate of growing = g = 3% = 3/100 = 0.03

Present value = P =?

The formula is as below:

P = [F/(r – g)] [1 – {(1 + g) / (1 + r)}^n]

= [1200/(0.08 – 0.03)] [1 – {(1 + 0.03) / (1 + 0.08)}^5]

= [1200 / 0.05] [1 – (1.03/1.08)^5]

= 24,000 × [1 – 0.953703^5]

= 24,000 × [1 – 0.788979]

= 24,000 × 0.211021

= 5,064.50 (Answer)

jeff jeffy answered 2 years ago

Next > < Previous

Related Solutions

An amount of $10,000 is deposited into a savings account that pays interest at a rate...

An amount of $10,000 is deposited into a savings account that pays interest at a rate of 7%. If 10 equal annual withdrawals are made from the account starting one year after the money was deposited, how much can be withdrawn so that in the fifth year one would be able to withdraw an additional $1,000 and the account would be depleted after 10 years? Explain verbally in detail and sketch a timeline to illustrate.

Determine how much $1,000 deposited in a savings account paying 8% (compounded annually) will be worth...

Determine how much $1,000 deposited in a savings account paying 8% (compounded annually) will be worth after 5 years. how would you insert this in a financial calculator? confused on how to input (FVIF .08,5)

A year ago, you deposited $30,000 into a retirement savings account at a fixed rate of...

A year ago, you deposited $30,000 into a retirement savings account at a fixed rate of 5.5 percent. Today, you could earn a fixed rate of 6.5 percent on a similar type account. However, your rate is fixed and cannot be adjusted. How much less could you have deposited last year if you could have earned a fixed rate of 6.5 percent and still have the same amount as you currently will when you retire 38 years from today?

On January 1, $5000 is deposited into a high-interest savings account that pays 8% interest compounded annually.

On January 1, $5000 is deposited into a high-interest savings account that pays 8% interest compounded annually. If all the money is withdrawn in 5 equal end-of-year sums beginning December 31 of the first year, how much will each withdrawal be?

A) Assume that you wish to make annual deposits into a savings account. The interest rate...

A) Assume that you wish to make annual deposits into a savings account. The interest rate offered by the bank is 11%, and you plan to save for the next 12 years. If your goal is for the present value of your savings to be equal to $4,058, how much money must you deposit every year? B) Assume you've just received a bonus at work of $3,812. You deposit that money in the bank today, where it will earn interest...

6.Suppose that you had savings deposited in an account at an interest rate of 5 percent...

6.Suppose that you had savings deposited in an account at an interest rate of 5 percent and your father told you that he earned 10 percent interest 20 years ago. Which of you was getting the better return? How would your answer change if you were told that the inflation rate in the United States was 12 percent 20 years ago and is 3 percent now? 7.Suppose you have $1,000, which you can put in two different types of accounts...

If $30,000 is deposited in a savings account at the end of each year and the...

If $30,000 is deposited in a savings account at the end of each year and the account pays interest of 5% compounded annually, what will be the balance of the account at the end of 10 years?

If you deposit $7,000 into a savings account with an annual interest rate of 5% annually...

If you deposit $7,000 into a savings account with an annual interest rate of 5% annually which is compounded monthly, What would be the value of the investment after 10 years? Please show your work.

Matt recently deposited $27,000 in a savings account paying a guaranteed interest rate of 4 percent...

Matt recently deposited $27,000 in a savings account paying a guaranteed interest rate of 4 percent for the next 10 years. A) If Matt expects his marginal tax rate to be 32.00 percent for the next 10 years, how much interest will he earn after-tax for the first year of his investment? B) How much interest will he earn after-tax for the second year of his investment if he withdraws enough cash every year to pay the tax on the...

Matt recently deposited $30,000 in a savings account paying a guaranteed interest rate of 5 percent...

Matt recently deposited $30,000 in a savings account paying a guaranteed interest rate of 5 percent for the next 10 years. If Matt expects his marginal tax rate to be 22 percent for the next 10 years, how much interest will he earn after-tax after the seventh year of his investment if he withdraws enough cash every year to pay the tax on the interest he earns? Dana intends to invest $25,000 in either a Treasury bond or a corporate...

Subjects