After Charlie Harper passed away, his brother Alan and Alan’s son Jake had to move out...

After Charlie Harper passed away, his brother Alan and Alan’s son Jake had to move out of Charlie’s beach house in Malibu where they had lived for so many years. Alan has just purchased a new apartment and financed this purchase with a 30-year mortgage that requires a 20% down payment. The rest is to be repaid in equal QUARTERLY installments of $2,200 each. The EAR on this mortgage is 6.5%, and the interest rate is compounded QUARTERLY. For accuracy, please retain three digits after the decimal point in interest rate computations in this problem (for example 5.123%).

a) What was the price of the apartment?

1 b) Suppose that Alan’s lender has to disclose the APR on this mortgage. What APR would the lender quote?

c) Based on the APR that you found in (b), which compounding frequency – daily (assuming 365 days), monthly, quarterly, semi-annual, or annual – would result in the highest EAR? Please find this EAR.

Solutions

Expert Solution

A	Loan	X amount
	Interest rate	6.5% pa	Quaterly 1.625%
	Installment Quaterly	2200
	Price of Apartment= ((x)/80)*100
	Loan amount= Qtrly installment* PVAF(1.625%, 120 Qtr)
	=2200*52.645	115819

	Price of apartment= 115819/.8	144773.8
	Total interst paid= 2200*120-115819	148181

B	APR=(Interest / Loan Amount)*365/ No. of days

	=(148181/115819)*(365/10950)
	4.26

C	Monthly= e^(.0426/365)^365 Working Finding out the value of e using calculator e=2.7183==> Sqrt 12 times==> 1.00024417206 e^{_{(0.0426/365)=}}_{.(.00024417206 x .1)+1 ===> Press (x &=) 12 times = 1.04352}	4.352%	Highest EAR Daily compounding
	Quaterly= (1.010651.010651.01065*1.01065)-1	4.328%
	Semi Annualy= (1.0213*1.0213)-1	4.305%
	Annualy	4.26%

jeff jeffy answered 1 year ago

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