Question

EAR & APR Question 8: You own Huntington Beach Boats, and just received a purchase for a $1.5 million yacht. Unfortunately, you have no money in your business account and need to borrow to build the boat! It will cost you $800,000 to build and you will be able to pay back the money in a year. Three banks you have visited are willing to give you the money with the boat as collateral if the buyer does not pay. CSUSB Credit Union is offering you an $800,000 loan at 12% simple interest. Huntington Beach Bank has offered you an $800,0000 loan at 11.8% compounded monthly. Finally, Bank of Laguna has offered you an 11% loan compounded continuously, for the same amount. Whose loan should you go with and what is the EAR of this loan? What is the APR of each loan?

Answer 1

Lets look at the following table:

Loan	Interest Type	Formula	Amount of interest	APR	EAR
CSUSB Credit union	Simple interest	Interest = (Principal x Rate x Time)/100	Interest = (800000 x 12% x 1)/100 Interest = 96000	APR = Interest/Principal x 100 96000/800000 x 100 = 12%	In case of simple interest, EAR, APR and the rate of interest given are all the same
Huntington	Compound interest (Monthly Compounding)	Interest = Amount- Principal $Amount = principal \times (1+\frac{rate}{t})^{nt}$ r = interest rate, t = 12 as monthly compounding, n = number of years	$899,676.57 = 800000 \times (1+\frac{0.118}{12})^{12}$	APR=Interest/Principal x 100 99,676.57/800000 x 100 = 12.46%	Here we need to calculate the EAR, wherein: $899,676.57 = 800000 \times (1+\frac{EAR}{1})^{1}$ EAR= 12.46%
Bank of Laguna	Compound interest (Continuous compounding)	Interest = Amount- Principal $Amount = principal \times \epsilon ^{rt}$ r = interest rate, t = time, e= exponential	$Amount = 800000 \times 2.718 ^{0.11 \times 1} = 893,022.46$	APR=Interest/Principal x 100 93022.46/800000 x100 = 11.62%	Here we need to calculate the EAR, wherein: $893022.46 = 800000 \times (1+\frac{EAR}{1})^{1}$ EAR= 11.62%

EAR is the rate which when used in annual compounding gives the same amount as in monthly or continuous compounding