Tillyard Inc. requires a $25,000 1-year loan. The bank offers to make the loan,
ID: 2749578 • Letter: T
Question
Tillyard Inc. requires a $25,000 1-year loan. The bank offers to make the loan, and it offers three choices: (1) 15 percent simple interest, annual compounding; (2) 13 percent nominal interest, daily compounding (365-day year); (3) 9 percent add-on interest, 12 end-of-month payments. The first two loans would require a single payment at the end of the year, the third would require 12 equal monthly payments beginning at the end of the first month. What is the difference between the highest and lowest effective annual rates?
6.00 percent points
4.25 percent points
2.48% percent points
3.58 percent points
5.00 percent points
a.6.00 percent points
b.4.25 percent points
c.2.48% percent points
d.3.58 percent points
e.5.00 percent points
Explanation / Answer
Effective Anual Interest Rate for 13% nominal rate with daily compunding
= (1 + 13%/365)365 = 13.88%
9% add on interest on $25,000 pricnipal with 12 monthly payments means an interest of 25000 * 9% = 2250 is added to the principal making it 25000 + 2250 = $27250.
Now this $27250 is paid in 12 monthly instalments of 27250/12 = $2270.83
Using the RATE function of excel, Monthly Rate can be calulated using the following syntax :
=RATE(12,-2270.83,25000,0)
The value comes out to be 1.35%, however, this is a monthly rate.
Effective Annual Rate = (1 + 1.35%)12 - 1 = 17.46%.
The difference between the highest and lowest effective annual rate
= 17.46% - 13.88% = 3.58%
Ans - d) 3.58 percent points