DigiCom wants to drop the effective rate of interest on its credit card by 2%. If it currently charges a nominal rate of 8% compounded daily, at what value should it set the new nominal rate? Note: Please make sure your final answer(s) are in percentage form and are accurate to 2 decimal places. For example 34.56%
The correct answer was: 6.14%
You should first calculate the effective rate with the formula:
f = (1 + i)m - 1
where f is the effective rate, i is the periodic rate, and m is the number of compoundings per year.
You shoud obtain 0.08%. Then you should change that rate and convert back by rearranging the formula.
i need help understanding how to get that same answer!
nvm...i got this...
m is 365 days in a year
I think you mean:
f = (1 + i)^m - 1 So to the power m
where i = nominal rate/365
i = .08/365
so
f = (1 +.08/365)^365 = 1.0833
so 8.33% is present effective rate
Now
we want to go down 2%
so
6.33 % is new effective rate
so
1.0633 = (1 + r/365)^365
log 1.0633 = 365 log (1 + r/365)
.00007302963 = log (1+ r/365)
1+r/365 = 1.000168171
r =.0614
or
6.14%
THNX again!!! :D
To find the new nominal interest rate, we need to follow these steps:
Step 1: Calculate the effective rate of interest
Using the formula f = (1 + i)^m - 1, where f is the effective rate, i is the periodic rate, and m is the number of compoundings per year.
In this case, the nominal rate is 8% compounded daily, so we convert it to a periodic rate by dividing it by the number of compoundings per year. Since there are 365 days in a year, the number of compoundings per year is 365. Therefore, the periodic rate is 8% / 365 = 0.0219.
Now we substitute this value into the formula to find the effective rate:
f = (1 + 0.0219)^365 - 1
f ≈ 0.08747
Step 2: Calculate the new nominal rate
Since DigiCom wants to drop the effective rate by 2%, we subtract 2% from the current effective rate:
0.08747 - 0.02 = 0.06747
Step 3: Convert the new effective rate to a nominal rate
To convert the new effective rate back to a nominal rate, we need to rearrange the formula.
f = (1 + i)^m - 1
Rearranging for i gives us:
(1 + i)^m = f + 1
1 + i = (f + 1)^(1/m)
i = (f + 1)^(1/m) - 1
Substituting the values we calculated:
i = (0.06747 + 1)^(1/365) - 1
i ≈ 0.0614
Therefore, the new nominal rate should be approximately 6.14%.