Henrietta went to a bank and obtained a personal loan with an interest rate of 3.18% compounded monthly. if the effective interest rate on the loan were to decrease by 1%, calculate the new nominal rate compounded monthly?
To calculate the new nominal interest rate compounded monthly, you need to follow these steps:
Step 1: Find the current nominal interest rate compounded monthly.
Given that Henrietta obtained a personal loan with an interest rate of 3.18% compounded monthly, the current nominal rate is 3.18%.
Step 2: Calculate the effective interest rate.
The effective interest rate is the actual interest rate taking into account the compounding period. For monthly compounding, you can use the formula:
Effective interest rate = (1 + (nominal interest rate / number of compounding periods))^number of compounding periods - 1
Plugging in the values, we get:
Effective interest rate = (1 + (3.18% / 12))^12 - 1
Effective interest rate = (1 + 0.0265)^12 - 1
Effective interest rate ≈ 0.0321724 or 3.2172%
Step 3: Find the new effective interest rate.
To calculate the new effective interest rate, we subtract 1% from the current effective interest rate.
New effective interest rate = current effective interest rate - 1%
New effective interest rate = 3.2172% - 1%
New effective interest rate = 2.2172%
Step 4: Calculate the new nominal interest rate compounded monthly.
Using the formula from Step 2, rearrange it to solve for the nominal interest rate:
Nominal interest rate = (1 + new effective interest rate)^(1 / number of compounding periods) - 1
Plugging in the values, we get:
Nominal interest rate = (1 + 2.2172%)^(1 / 12) - 1
Nominal interest rate ≈ 0.1796 or 17.96%
Therefore, the new nominal interest rate compounded monthly would be approximately 17.96%.