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 same answer.
To find the new nominal rate, you need to add 0.50% to the effective rate. Here's how you can calculate it:
1. Start with the given nominal rate: 4.25% compounded semi-annually.
2. Convert the nominal rate to an effective rate by dividing it by the number of compounding periods per year. In this case, the compounding is semi-annually, so there are two periods per year.
Effective rate = Nominal rate / Number of compounding periods
Effective rate = 4.25% / 2 = 2.125%
3. Add the desired increase of 0.50% to the effective rate:
New effective rate = Effective rate + Desired increase
New effective rate = 2.125% + 0.50% = 2.625%
4. Convert the new effective rate back to a nominal rate using the same number of compounding periods:
New nominal rate = New effective rate * Number of compounding periods
New nominal rate = 2.625% * 2 = 5.25%
So, Swan Furnace Cleaners should set the new nominal rate to 5.25% in order to achieve an effective rate increase of 0.50%.