Question

Cersei has not budgeted wisely. As a result, she needs a quick loan from the Iron Bank. Cersei needs $1.5 million and the Iron Bank has agreed to lend her the $1.5 million if she makes 4 quarterly payments in the amount of $500,000 each, to be paid at the end of each quarter starting in three months (at the end of the first quarter). Cersei is about to agree to the terms, but then her brother Jamie says that he will lend her a hand by loaning the money she needs, and he will charge her an effective annual rate that is lower than the effective annual rate of the loan from the Iron Bank. However, neither Jamie nor Cersei knows how to calculate the effective annual rate for this loan, so they have turned to you for help. What is the effective annual rate (E.A.R.) on the loan from the Iron Bank based on the terms above?

Answer 1

Amount borrowed = $1,500,000
Quarterly payment = $500,000
Number of payments = 4

Let quarterly interest rate be i%

$1,500,000 = $500,000 * PVA of $1 (i%, 4)

Using financial calculator:
N = 4
PV = 1500000
PMT = -500000
FV = 0

I = 12.59%

Quarterly interest rate = 12.59%

Effective annual rate = (1 + Quarterly interest rate)^4 - 1
Effective annual rate = (1 + 0.1259)^4 - 1
Effective annual rate = 1.6069 - 1
Effective annual rate = 0.6069 or 60.69%

Therefore, Iron Bank is offering loan to Cersei at 60.69% effective annual rate.