Question

In: Finance

1.) You plan to deposit $1,000 in Year 1, $1,200 in Year 2 and $2,000 in...

1.) You plan to deposit $1,000 in Year 1, $1,200 in Year 2 and $2,000 in year 4 in your savings account. You think that you can earn 6% per year. How much will you have in your account in Year 6?

2.) Bank X promises to pay you $5,200 per year for 8 years, whereas Bank Y offers to pay you $7,300 per year for 5 years.

a) Which of these cash flow streams has the higher present value (PV) if the discount rate is 5 percent? (Hint: compare the PVs of annuity X ($5,200 per year for 8 years) with annuity B ($7,300 per year for 5 years)

b) Which one should you choose between Bank X and Bank Y?

3.) Today, Dinero Bank offers you a $60,000, five-year term loan at 7.5 percent annual interest (APR). What will your annual loan payment be? (Hint: Find PMT)

4.) You buy an annuity that will pay you $24,000 a year for 25 years. The payments are paid on the first day of each year. What is the value of this annuity today if the discount rate is 8.5 percent? (Hint: annuity due)

SHOW HOW YOU GOT ANSWERS PLEASE!!

Solutions

Expert Solution

(1) NOTE: Assumption - Deposits are made at the end of the Years mentioned

Year 1 Deposit = $ 1000, Year 2 Deposit = $ 1200 and Year 4 Deposit = $ 2000 and Interest Rate = 6 %

Future Value of Deposits at the end of Year 6 = 1000 x (1.06)^(5) + 1200 x (1.06)^(4) + 2000 x (1.06)^(2) = $ 5100.398

(2) Bank X: Annuity = $ 5200, Interest Rate = 5 %, Tenure = 8 years

PV of Annuity = PV(x) = 5200 x (1/0.05) x [1-{1/(1.05)^(8)}] = $ 33608.71

Bank Y: Annuity = $ 7300, Interest Rate = 5 %, Tenure = 5 years

PV of Annuity = PV(y) = 7300 x (1/0.05) x [1-{1/(1.05)^(5)}] = $31605.18

As PV(x) > PV(y), the investor should chose Bank X over Bank Y.

(3) Initial Loan Amount = $ 60000, Loan Tenure = 5 years and Interest Rate = 7.5 %

Let the PMT be $ K

Therefore, 60000 = K x (1/0.075) x [1-{1/(1.075)^(5)}]

60000 = K x 4.046

K = $ 14829.88

(4) Annuity Due = $ 24000, Tenure = 25 years, Discount Rate = 8.5 %

PV of Annuity Due = 24000 x (1/0.085) x [1-{1/(1.085)^(25)}] x (1.085) = $ 266498.3  


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