Question

In: Finance

Jody wants to save for her college expenses. She received a$6,000 gift from her grandparents...

Jody wants to save for her college expenses. She received a $6,000 gift from her grandparents at age 10 and wants to see it increase to $9,000 by the time she turns 15. If she invests all of her gift, what rate of return should be expected to reach her goal of $9,000? For 5 extra credit points, instead of a $6,000 gift, 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

Calculating Rate of Interest and Present Value of Annuity

a.)Future Value of Single Payment =>

FVn = PV(1+r)n

9000 = 6000(1+r)5

1.5 = (1+r)5

1.51/5 = 1+r

r = 1.084475-1

r = 8.4475%

Please note that r can be calculated with Trial and Error method.

b.) Present Value of a Growth Annuity=>

Formula =

=

=  

= 5064.48

Here: P - Annual Payment

r - rate of interest

g - growth rate

n - number of period


Related Solutions

Sophia inherits inherited money from her grandparents. She inherits $100,000 from her grandparents, today. She has...
Sophia inherits inherited money from her grandparents. She inherits $100,000 from her grandparents, today. She has exactly 20 years to retire and she decided to put the entire amount into 20 years, 4% annual interest annuity. A) Assume that she did not deposit any additional amount into this account, compute your account balance by the time she retires. Please compute the problem using a scientific calculator (not a financial one) using the appropriate formulas and show your calculations step by...
Yumi's grandparents presented her with a gift of $21,000 when she was 12 years old to...
Yumi's grandparents presented her with a gift of $21,000 when she was 12 years old to be used for her college education. Over the next 5 years, until she turned 17, Yumi's parents had invested her money in a tax-free account that had yielded interest at the rate of 2.5%/year compounded monthly. Upon turning 17, Yumi now plans to withdraw her funds in equal annual installments over the next 4 years, starting at age 18. If the college fund is...
Y received stock as a gift from her father in 2019. Her father purchased the stock...
Y received stock as a gift from her father in 2019. Her father purchased the stock several years ago of $30,000. The stock was worth $20,000 at the time the gift was received. Y sold the stock for $18,000 in 2020. How much gain or loss, if any, should Y report on her 2020 tax return? Assume the same facts as above, except that Y sold the stock for $25,000. How much gain or loss, if any, should Y report...
Taylor has just received an insurance settlement of $58,400. She wants to save this money until...
Taylor has just received an insurance settlement of $58,400. She wants to save this money until her oldest daughter goes to college. Taylor can earn an average of 5.5 percent, compounded annually, on this money. How much will she have saved for her daughter's college education if her daughter enters college 14 years from now? a. $123,579.74 b. $108,153.58 c. $82,990.77 d. $187,302.09 e. $110,459.16
Elaine has just received an insurance settlement of $25,000. She wants to save this money until...
Elaine has just received an insurance settlement of $25,000. She wants to save this money until her daughter goes to university. If she can earn an average of 6.5%, compounded annually, how much will she have saved when her daughter enters university eight years from now?
Jody is interested in the population mean of pets per household in her neighborhood. She hypothesized...
Jody is interested in the population mean of pets per household in her neighborhood. She hypothesized that the average amount of pets per household will be less than 3. To test the hypothesis, she used the following data. 0 1 3 2 1 3 1 0 4 1 0 5 1 2 0 1 2 1 Jody's hypotheses are H0 : µ≥3 HA : µ<3 Please calculate 1) null and alternative hypothesis 2) alpha value 3) p-value 4) conclusion
Your grandparents deposited $12,000 into an account for you 17 years ago for college expenses. The...
Your grandparents deposited $12,000 into an account for you 17 years ago for college expenses. The account balance grew to $24,000. What rate of return (in percentage) was their deposit earning, annually?
Laura Drake just inheritance some cash from her late grandparents. She is considering to invest the...
Laura Drake just inheritance some cash from her late grandparents. She is considering to invest the cash into either of two bond outstanding. Both bonds do have par value of $1,000 and 11 percent coupon paid annually. Bond A do have 10 years to maturity while bond B have 5 years to maturity. * (a) Determine the value of bond A in the required returns is (i) 8 percent, (ii) 11 percent and (iii) 14 percent. (b) Determine the value...
Jessica inherited a $1000 portfolio of investments from her grandparents when she turned 21 years of...
Jessica inherited a $1000 portfolio of investments from her grandparents when she turned 21 years of age. The portfolio is comprised of the following three investments:                                                 expected return                         dollar value Treasury bills                            4.5%                                        $40,000 Ford (F)                                    8.0%                                        $30,000 Harley-Davidson (HOG)            12%                                         $30,000 a. Based on the current portfolio composition and the expected rates of return, what is the expected rate of return for Jessicas portfolio? b. If Jessica wants to increase her expected portfolio rate of return, she could...
Maria received a gift of stock from her favorite uncle. The stock had a fair market...
Maria received a gift of stock from her favorite uncle. The stock had a fair market value of $40,000 and a basis to the uncle of $10,000 at the date of the gift. Is the gift taxable to Maria? If so, how much is taxable? Is the gift taxable to to the uncle? If so, how much is taxable? If the uncle sold the stock and gave the proceeds as a gift to Maria would the gift be taxable to...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT