Dwelling on Deposits - Assignment Example

How much should you deposit today in order to withdraw $4,000 per year for 7 years? You're first to withdraw will start 6 years from now and your deposit will earn 2% interest.

Data: FV =  $4000                                            PMT = ?

            i =  2%

4000 [1/(1 + 0.02)]1

= $3921.56

Which amount is worth more at 10%: $1,000 in hand today or $2,000 due in five years?

In which case we are going to determine the present value of $2,000 due in five years

FV=PV(1+i)n

Hence

PV=FVt[ 1/(1+R)n]

2000 [1/(1 + 0.10)]5

2000(0.6209) = 1241.84
1241.84 is greater than $1,000 hence $2,000 due in five years is worth more.

What is Krystal’s annual percentage rate (APR) and EAR?

APR

FV = 180,000

PV = 150000

N = 17 months

FV=PV(1+i)n

180,000/150000 = (1 + i)17

1 + i = 10.60

APR = I = 10.60 – 1 = 9.60%

EAR = [(1+(i/m)]m –   1    =   [(1+(.096/17)]17 –1 = 0.10 = 10%

• P/Y = 12, N = 20 ´ 12 = 180, I = 7%, PMT = 50000,

PVA=PMT(1-(1+i)-n)/i

PVA=50000(1-(1+0.07)-9)/0.07

= $28,000

Suppose you are going to buy a car. The cost of car is $20,000. You have $8,000 for down payment. You can borrow the balance of $12,000 from dealership’s finance company at 2% APR, with monthly payment for 36 months or you can borrow from a bank with 8% APR monthly payment for 3 years, and receive a $2,000 rebate on the purchase price. Assume that if you take the rebate, you will apply it toward the purchase. Which alternative is better deal?

ALTERNATIVE 1

ALTERNATIVE 2

Hence alternative 2 allowing for rebate is the best.

You are preparing for a vacation to Europe in the future. You plan to save $400 a month beginning today and estimate you earn 0.5% per month on your savings. Your goal is to save $6,000. How long does it take to save this amount?

FV = $6,000

PV  = $400
I= 0.5%

N = ?

FV=PV(1+i)n

$6,000 = $400(1 + 0.005)n

15 = (1 + 0.005)n

Log 15 = n log 1.005

1.176 = 0.002166 n

N = 542 months

= 45 years

What is the present value of a perpetuity of $100 per year if the appropriate discount rate is 5%? If the discount rate is increased to 15% what is the present value of the perpetuity?

Present Value (PV) of Perpetuity = A/r

A = $100

r = 5%

= 100/0.05

$2000

If increased to 15%

100/0.15

$666.66

Bank of Land has a student loan program starting today but requires no payments for 4 years. However, during this interest deferred period the loan accumulated interest at a 6% rate, compounded quarterly. The bank amortizes the loan over ten year period, requiring quarterly payments and continuing charge a 6% annual interest rate, compounded quarterly. What will be the quarterly payment will be on today’s loan of $30,000?

Hence quarterly

FV365 = $1,000 x (1.00032877)365= $1,000 x (1.12747) = $1,127.47.
 

Energy Tech company issued an 8% (semiannual payment) 15 year bond 5 years ago.
If the yield of similar bond today is 6%, what is the bond price? What is the current yield?
If you expect company to call the bond 3 years from today and will pay the principal plus two years coupon interests as penalty. What price you should pay for this bond

PV = C/(1+i) + C/(1+i)2 + … + C/(1+i)n + F/(1+i)n

Plugging in the above information gives:

$2,000 = $100/(1+i) + $100/(1+i)2 + … + $100/(1+i)20 + $1000/(1+i)20

i = 3%. 

Green Co. just paid a dividend of $1 per share. The company predicts that the dividend will increase 5% for the next 5 years and 3% thereafter forever. If your required rate of return is 8%, what price you should pay for the stock?

Pb=INT/(1+rd)+ INT/(1+rd)2+…. INT/(1+rd)N+ M/(1+rd)N

Price =  ($1/(0.08 - 0.05)) +  ($1/(0.08 - 0.03)

= 33.33 + 20  =$ 53.33