Swan Furnace Cleaners wants to add 0.50% to the effective rate of interest on its credit card. If it currently charges a nominal rate of 4.25% compounded semi-annually, at what value should it set the new nominal rate?
The answer for this question is 4.74%,
the formula for this question is
f=(1+i)^m
=total - 1
I know that j=4.25%
m=2
i=j/m=.0425/2=.02125=2.125%
f=(1+.02125)^2 -1
=0.042951562
=4.30%
but the right answer is 4.74%, i cant seem to figure out how to get that answer.
you had an effective annual rate of
.042951563 which I agree with.
didn't it say they wanted to increase that effective rate by .5% or by .005
so .04295 + .005 = .04795 = 4.795%
(So I guess I disagree with their answer)
it said after i find the efffective rate i should chage that rate and convert bacck by rearranging the formula.
:S
very confusing
im sry...but ure wrong...:-(...but still thnx though:)
To find the new nominal rate, you need to use the formula for the effective rate of interest. Let's break down the problem step by step:
1. Start with the existing nominal rate, which is 4.25% compounded semi-annually.
2. Convert the nominal rate to the periodic interest rate. Since compounding is done semi-annually, divide the annual interest rate by 2:
i = 4.25% / 2 = 2.125%
3. Now, you need to find the effective interest rate. Use the formula:
Effective interest rate = (1 + i)^m - 1,
where i is the periodic interest rate (2.125%) and m is the number of compounding periods per year (2 for semi-annual compounding).
4. Calculate the effective interest rate:
Effective interest rate = (1 + 0.02125)^2 - 1
= (1.02125)^2 - 1
= (1.0438678) - 1
= 0.0438678 (rounded to 7 decimal places) or 4.39% (rounded to 2 decimal places).
5. Finally, to add 0.50% to the effective interest rate, simply add 0.005 to the result:
New effective interest rate = 0.0438678 + 0.005
= 0.0488678 (rounded to 7 decimal places) or 4.89% (rounded to 2 decimal places).
Therefore, the new nominal rate should be set at 4.89% compounded semi-annually, which is the closest answer to 4.74% that you mentioned.