Megan Green is interested in taking out a personal loan for $1,550. However, last year an identity theft scam left her with poor credit. Since then she has learned about the perils of identity theft from personal experience as well as from a variety of sources, including the August 18, 2009, article “Avoiding the Identity Theft Underworld� on a website. Because of the resulting poor credit score due to the identity theft and the fact that she is providing no collateral, the bank is going to charge her a fee of 3.0% of her loan amount as well as take out the interest upfront. The bank is offering her 16% APR for six months.
Calculate the effective interest rate. (Use 360 days a year. Do not round intermediate calculations and round your final answer to the nearest whole number. Omit the "%" sign in your response.)
To calculate the effective interest rate, we need to take into account both the upfront fee and the interest charged.
First, let's calculate the upfront fee on the loan:
Upfront fee = 3.0% of $1,550 = $46.50
Next, let's calculate the interest charged on the loan:
Interest = Principal * Rate * Time
= $1,550 * 16% * (6/12)
= $124.00
Now, let's calculate the total amount charged on the loan, which includes the upfront fee and the interest:
Total amount charged = Principal + Upfront fee + Interest
= $1,550 + $46.50 + $124.00
= $1,720.50
To calculate the effective interest rate, we need to find the rate that would result in the same total amount charged over a one-year period with monthly compounding. We'll use the formula:
Effective interest rate = (Total amount charged / Principal)^(1/Time) - 1
Here, Time is in years, so for our calculation, Time would be 6 months divided by 12 months.
Effective interest rate = ($1,720.50 / $1,550)^(1/(6/12)) - 1
= 1.111935 - 1
= 0.111935
To convert the decimal to a percentage, we multiply by 100:
Effective interest rate = 0.111935 * 100
= 11.1935
Rounding to the nearest whole number, the effective interest rate is approximately 11%.