Warm-Up Excercises: 1. Assume a firm makes $2,500 deposit into its money market
ID: 2668597 • Letter: W
Question
Warm-Up Excercises:1. Assume a firm makes $2,500 deposit into its money market account. If this account is currently paying 0/7% ( yes, that’s right, less than 1%!), what will the account balance be after 1 year?
2. If Bob and Judy combine their savings of $ 1,260 and $ 975, respectively, and deposit this amount into an account that pays 2% annual interest, compounded monthly, what will the account balance be after 4 years?
3. Gabrielle just won $ 2.5 million in the state lottery. She is given the option of receiving a total of $ 1.3 million now, or she can elect to be paid $100,000 at the end of each of the next 25 years. If Gabrielle can earn 5% annually on her investments, from a strict economic point should she take?
4. Your firm has the option of making an investment in new software that will cost $130,000 today and is estimated to provide the savings shown in the following table over its 5-year life:
Year Saving Estimate
1 $ 35,000
2 50,000
3 45,000
4 25,000
5 15,000
Should the firm make this investment if it requires a minimum annual return of 9%
on all investment?
5. Joseph is a friend of yours. He has plenty of money but little financial sense. He received a gift of $ 12,000 for this recent graduation and is looking for a bank which to deposit the funds. Partner’s Savings Bank offers an account with annual interest rate of 3% compounded semiannually, while Selwyn’s offers an account with a 2.75% annual interest rate compounded continuously. Calculate the value of the two accounts at the end of one year, and recommend to Joseph which account he should choose.
6. Jack and Jill have just had their first child. If college is expected to cost $ 150,000 per year in 18 years, how much should the couple begin depositing annually at the end of each year to accumulate enough funds to pay the first year’s tuition at the beginning of the 19th year? Assume that they can earn a 6% annual rate of return on their investment.
Explanation / Answer
1. Assume a firm makes $2,500 deposit into its money market account. If this account is currently paying 0/7% ( yes, that’s right, less than 1%!), what will the account balance be after 1 year? We know AMount = Principal*(1+i)^n where i = annual IntRate & n is period in yrs So we get AMount = 2500*(1+0.7%)^1 = $2,517.50 ............Ans 2. If Bob and Judy combine their savings of $ 1,260 and $ 975, respectively, and deposit this amount into an account that pays 2% annual interest, compounded monthly, what will the account balance be after 4 years? Total Principal = 1260+975 = $2,235.00 We know AMount = Principal*(1+i/p)^(n*p) where i = annual IntRate, p = times compunded & n is period in yrs So we have i=2%, p=12 as monthly, n=4 yrs Putting values, we get AMount = 2235*(1+2%/12)^(4*12) = $2,420.99 or $2421 3. Gabrielle just won $ 2.5 million in the state lottery. She is given the option of receiving a total of $ 1.3 million now, or she can elect to be paid $100,000 at the end of each of the next 25 years. If Gabrielle can earn 5% annually on her investments, from a strict economic point should she take? Here we have to calculat ethe PV of annuity of PMT=$100,000 for n=25 Yrs & i=5% PV of annuity = PVA = Present value of annuity due PVA = PMT(PVIFAi,n) So PVA = PMT*(1/i - 1/(i(1+i)^N)) So PVA = 100000*(1/5% - 1/(5%*(1+5%)^25)) = $1,409,394 So PV of Future Cash payments at $1,409,394 is higher than $1,300,000 which she is being offered now. SO she should opt for Annual payment of $100,000 if she doesn;t need the Lump sum payment now. 4. Your firm has the option of making an investment in new software that will cost $130,000 today and is estimated to provide the savings shown in the following table over its 5-year life: Year Saving Estimate 1 $ 35,000 2 50,000 3 45,000 4 25,000 5 15,000 Should the firm make this investment if it requires a minimum annual return of 9% on all investment? Net Present value of this investment = NPV(Rate, Cash Flows) + Initial Cash outflow ie NPV = NPV(9%,35000,50000,45000,25000,15000)-130000 = $6,402 As NPV is positive, Firm should make the Investment 5. Joseph is a friend of yours. He has plenty of money but little financial sense. He received a gift of $ 12,000 for this recent graduation and is looking for a bank which to deposit the funds. Partner’s Savings Bank offers an account with annual interest rate of 3% compounded semiannually, while Selwyn’s offers an account with a 2.75% annual interest rate compounded continuously. Calculate the value of the two accounts at the end of one year, and recommend to Joseph which account he should choose. Principal = $12000 We know AMount = Principal*(1+i/p)^(n*p) where i = annual IntRate, p = times compunded & n is period in yrs Partner SB : So we have i=3%, p=2 as Semi-annualy, n=1 yrs Putting values, we get AMount = 12000*(1+3%/2)^(1*2) = $12,362.70 ....(1) Selwyn SB: So we have i=2.75%, p=365 as continuous , n=1 yrs Continuous Compounding Formula Int Rate r =Ln(1+ i) where Ln is Natural Log So we get Int rate r = Ln(1+2.75%) = 2.7129% Putting values, we get AMount = 12000*(1+2.7129%)^1 = $12,325.55 ....(2) So he should chosse Partner SB which gives a higher return 6. Jack and Jill have just had their first child. If college is expected to cost $ 150,000 per year in 18 years, how much should the couple begin depositing annually at the end of each year to accumulate enough funds to pay the first year’s tuition at the beginning of the 19th year? Assume that they can earn a 6% annual rate of return on their investment. Here we have to find Annual Payments PMT reqd. FV of Annuity FVA = $150,000, Peiod n=18 yrs, Int Rate i=6% FVAn= PMT(FVIFAi,n) So we have FVAn = PMT*[(1+i)^n-1]/i Putting values we get 150000 = PMT*((1+6%)^18 - 1)/6% = 30.9057*PMT So PMT = $4,853.48 So Annual payment reqd is $4,853.48