You need to borrow $275,000 for 4 months at a stated rate of 6.5%. 1. What the e
ID: 2752518 • Letter: Y
Question
You need to borrow $275,000 for 4 months at a stated rate of 6.5%.
1. What the effective annual interest rate? and Why is the effective annual interest rate higher than the stated rate of 6.5%?
2. What if you needed to borrow $275,000 for 2 months at the same stated rate of 6.5%. What is the effective annual interest rate? Why is the new effective rate higher than the effective rate in the first scenario?
Amount borrowed $275,000 Annual Interest Rate 6.5% Length of Loan (months) 4 Loan Periods in a Year 3 Dollar Amount of Interest $5,9581. What the effective annual interest rate? and Why is the effective annual interest rate higher than the stated rate of 6.5%?
2. What if you needed to borrow $275,000 for 2 months at the same stated rate of 6.5%. What is the effective annual interest rate? Why is the new effective rate higher than the effective rate in the first scenario?
Explanation / Answer
Answer (1)
Effective annual rate = 6.64%
Effective rate of interest is the rate applicable on simple basis when the compounding period is less than a year. Effective rate annual rate is higher than annual rate of interest because of the compounding of interest, that is calculation of interest on interest is done for a period less than one year and hence result in a higher interest income.
Answer (2)
Effective annual rate = 6.68%
This effective annual rate is higher than that for a compound period of 4 months calculated above. The new effective rate is higher than the earlier effective rate as the number of compounding periods increases, the time for which we earn interest on interest increases. This results in a higher interest on interest and hence higher effective annual rate.
Annual interest rate = 6.5% or 0.065
Loan period in a year = 3 = This means compounding is done thrice a year
Effective rate of interest is the rate applicable on simple basis when the compounding period is less than a year.
In this case effective rate can be calculated as follows
Effective rate of interest = (((1+ rate of int / 3)^no of years * no of compounding periods) -1) *100
Here
number of years = 1
number of compounding periods = 3
Effective rate of interest = [(1+ 0.065/3)^1 * 3 – 1] * 100
= [(1+0.021666667)^3 - 1] * 100
= [1.0664185 – 1] * 100
= 6.64185 or 6.64% (rounded off)
If the loan is to be taken for 2 months, then the compounding period is 2 months.
Hence Number of years = 1
Number of compounding periods = 12 Months/ 2 months = 6
Effective rate applicable for a 2 month loan where compounding is done on a bi-monthly basis can be calculated as follows
Effective rate of interest = [(1+0.065/6)^1*6 – 1]*100
= [(1+0.01083333)^6 - 1]*100
= [(1.01083333)^6 – 1]*100
=[1.066786 – 1]*100
= 6.6786% or 6.68% (rounded off)
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