Question

Tillyard Inc. requires a $25,000 1-year loan. The bank offers to make the loan, and it offers you three choices: (1) 15 percent simple interest, annual compounding; (2) 12 percent nominal interest, daily compounding (360-day year); (3) 10.2 percent add-on interest, 4 end-of-quarter payments. The first two loans would require a single payment at the end of the year, the third would require 4 equal quarterly payments beginning at the end of the first quarter. What is the difference between the highest and lowest effective annual rates?

Answer 1

1) Here since it is simple interest annual compounding effective annual rate = 15%

2) effective annual interest rate Daily compounding = [1+(r/n)]^n - 1

here r = rate of interest = 12%

n = number of periods = 360

so effective annual rate = [1+(12/360)]^360 - 1

= 12.7474%

3) here first lets find out total amount to be repaid

amount to be repaid = 25,000(1.102) = 27,550

since it is quarterly payment periodic payments = 27550 / 4 = 6887.5

now we have to calculate quarterly interest rate using financial calculator

enter, N = 4 ; PV = 25000; PMT = -6887.5 FV = 0 and find the value of I

interest = 4.002%

how ever this is quarterly rate,annual rate = (1.04002)^4 - 1 = 17%

hence difference between highest and lowest EAR  = 17 - 12.7474

= 4.25% (rounded to two decimals)