SOLUTION: A property worth $35 OOO is purchased for 10% down and semi-annual payments of $2100 for 12 years. What is the nominal annual rate of interest if interest is compounded quarterly?

Question 1207420: A property worth $35 OOO is purchased for 10% down and semi-annual payments of $2100 for 12 years. What is the nominal annual rate of interest if interest is compounded quarterly?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
30% down on 35000 is 3500.
amount to be financed is 35000 - 3500 = 31500.

using the texas instruments business analyst calculator, i get the the semi-annual effective interest rate is 4.160152395%.

the decimal equivalent of that is .04160152395.

add 1 to it to get the semi-annual effective growth factor equal to 1.04160152395.

take the square root of that to get the quarterly effective growth factor equal to 1.020588812.

to confirm the semi-annual growth factor and the quarterly growth factor are equivalent, do the following:

raise the quarterly growth factor to the fourth power to get the effective annual growth factor equal to 1.084933735.

raise the effective semi-annual growth factor to the second power to get the effective annual growth factor equal to 1.084933735.

both the semi-annual and the quarterly effective growth rate give you the same annual effective growth factor, as they should.

since you are working with quarterly compounding, do the following:

the quarterly effective interest rate is equal to the quarterly effective growth rate minus 1 which is equal to .020588812.

the annual nominal interest rate (not the annual effective interest rate) is equal to that * 4 = .08235525.
that's your nominal annual interest rate.

multiply that by 100 to get 8.235525%.
that's the same interest rate in percent form.

if this confuses you, or if my answer doesn't agree with the answer you are sup9osed to get, then get in touch with me with the answer you're supposed to get and i can work to determine where the discrepancy lies.

the complication in your problem is that you are making semi-annual payments when your interest rate is compounded quarterly.

normally those are in sync, i.e. quarterly payments with quarterly compounding, or semi-annual payments with semi-annual compounding.

when you have semi-annual payments with quarterly compounding, then it's required to get the equivalent semi-annual interest rate, which is what i did above.

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