You bought a $4,000 used car with no down payment and agreed to pay for it with

Question

You bought a $4,000 used car with no down payment and agreed to pay for it with a single payment of $4,781 after 3 years. Assuming compounding every 4 2. months: a) b) What is the interest rate charged per interest period on this transaction? 4 What are the nominal and effective interest rates? Assume that you have a credit card whose statement on June 1 showed that you owe $1,720.00. You made a payment to the credit card company of $600.00 on the same day using on-line payment. Throughout the month of June you charged 3. $295.00 on this card which is posted on the July 1 statement. On July 1 you made an on-line payment of $730.00 to the company. Throughout the month of July you charged $530.00 on this card which is posted on August 1. a) Draw a timeline showing this cash flow. 2 b) How much do you owe the credit card company on August 1? Assume the company charges 2% per month. Show all calculations

Explanation / Answer

(2)

Number of compounding periods (quarters) = 3 x 4 = 12

(a) If quarterly interest rate be r%,

$4,000 x (1 + r)12 = $4,781

(1 + r)12 = $4,781 / $4,000 = 1.1953

Taking 12th root on each side,

1 + r = 1.0150

r = 0.0150

r = 1.5% per quarter

(b)

Nominal (annual) interest rate = 1.5% x 4 = 6%

Effective interest rate = (1 + Quarterly interest rate)4 - 1 = (1.015)4 - 1 = 1.0614 - 1 = 0.0614 = 6.14%

NOTE: As per Answering Policy, 1st question has been answered.

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