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Company A takes a $750000 loan at a 8% APR rate with quarterly compounding
Company A takes a $750000 loan at a 8% APR rate with quarterly compounding. If the company takes 10% and puts it in an interest-bearing account. The bank that serve the firm pays 1% APR with quarterly compounding. What is the EAR of firm three-month loan? What will be the effective payment?
Expert Solution
Computation of EAR of Firm Three-month loan:
Value of the loan after 3 months = $750,000 * (1 + (8%/4))
= $750,000 * (1 + 2%)
= $765,000
Amount of loan deposited in the interest bearing account = Loan Amount * Interest Rate
= $750,000 * 10%
= $75,000
Interest earned = $75,000 * (1%/4)
= $75,000 * 0.25%
= $187.50
Effective loan value after three months = Value of the loan after 3 months - Interest earned
= $765,000 - $187.50
= $764,812.50
EAR = ($764,812.50/$750,000)^4 - 1 = 8.14%
Effective Payment = Effective loan value after three months - Loan amount
= $764,812.50 - $750,000
Effective Payment = $14,812.50
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