Question

On 31 August 2018, SisterCo issued a 180-day bank bill with a face value of $100,000 at a yield of 5.5% p.a. The bill was accepted and discounted by BankOne on that date. BankOne held the bill for 97 days and then sold it to BankTwo at a yield of 5.9% p.a. How much did BankOne receive when it sold the bill to BankTwo? Round your answer the whole dollar

A.

$95,897

B.

$98,989

C.

$97,676

D.

$98,676

E.

$96,783

You want to buy a new car and are considering a payment plan where you will make monthly payments of $1,000 for two years, starting at the end of this month. You have been quoted a rate of 5.5% p.a. compounding semi-annually. What is the price of the car today? (Round your answer to the whole dollar)

A.

$29,345

B.

$22,692

C.

$20,001

D.

$24,968

E.

$25,894

Answer 1

1)

Amount Received by BankOne = PV of Face Value before 180-97 = 83 days

Interest Rate for 83 days = 0.059*83/365 = 0.0134

PV = FV/[1+Interest Rate] = 100000/[1+0.0134] = 98676.12 = (D) $98676

2)

Effective Interest Rate or EAR = [{1+(APR/n)}^n]-1

Where, APR = Annual Interest Rate or Nominal Rate, n = Number of times compounded in a year

Therefore,

For Semi Annual,

EAR = [{1+(0.055/2)}^2]-1 = 0.055756

For Monthly,

0.055756 = [(1+i)^12]-1

1.055756 = (1+i)^12

i = (1.055756^1/12)-1 = 0.00453

PV of Annuity = P*[1-{(1+i)^-n}]/i

Where, P = Annuity = 1000, i = Interest Rate = 0.00453, n = Number of Periods = 2*12 = 24

PV = 1000*[1-{(1+0.00453)^-24}]/0.00453 = 1000*0.10283/0.00453 = 22692.76 = (B) $22692