Question

You are the accounting manager for Kool Ragz, Inc., a manufacturer of men's and women's clothing. The company needs to borrow $1,300,000 for 90 days in order to purchase a large quantity of material at "closeout" prices. The interest rate for such loans at your back, Rimrock Bank, is 14% using ordinary interest.

a.) What is the amount (in $) of interest on this loan? $______
b.) After making a few "shopping" calls, you find that Southside National Bank will lend at 14% using exact interest. What is the amount (in $) of interest on this offer?
$_________
c.) So that it can keep your business, Rimrock Bank has offered a loan at 13.5% using ordinary interest. What is the amount (in $) of interest on this offer?
$__________
d.) (Challenge) If Southside National wants to compete with Rimrock's last offer (part c) by charging $1,875 less interest, what rate (as a %), rounded to the nearest hundredths of a percent, must it quote using exact interest?
________%

Answer 1

a.) The interest on the loan from Rimrock Bank is $51,506.85. b.) The interest on the offer from Southside National Bank is $52,000. c.) The interest on the offer from Rimrock Bank at 13.5% is $50,684.93. d.) Southside National Bank must quote an interest rate of 14.59% to compete with Rimrock Bank's offer.

Step-by-step explanation:

a.) The amount of interest on this loan can be calculated using the formula: Interest = Principal x Rate x Time. In this case, the principal is $1,300,000, the rate is 14%, and the time is 90/365 (since it is a 90-day loan). Therefore, the interest on this loan is $51,506.85.

b.) For the offer from Southside National Bank, the interest can be calculated using the same formula. The principal is still $1,300,000, the rate is still 14%, but the time is now exact, which means it is 90/360. Therefore, the interest on this offer is $52,000.

c.) To calculate the interest on Rimrock Bank's offer at 13.5% using ordinary interest, the formula remains the same. The principal is still $1,300,000, the rate is now 13.5%, and the time is still 90/365. Therefore, the interest on this offer is $50,684.93.

d.) To determine the interest rate that Southside National Bank must quote in order to compete with Rimrock Bank's offer in part c, we can set up the equation: $51,506.85 - $1,875 = $52,000 x Rate x 90/360. By solving for the rate, we find that it must be 14.59% (rounded to the nearest hundredth).

Answer 2

Kool Ragz, Inc. can assess different loan offers by calculating the interest amounts using various rates and methods. The interest would be $45,500 at a 14% ordinary interest rate, $44,246.58 using exact interest, and $43,312.50 at a reduced rate of 13.5% with ordinary interest. For Southside National to compete, their rate would need to be approximately 11.55% using exact interest.

Step-by-step explanation:

Calculating Loan Interest

Let's break down each part of your question and calculate the interest on the loans being considered by Kool Ragz, Inc. from different banks using their respective rates and interest calculation methods.

a.) Interest using ordinary interest at 14% on a $1,300,000 loan:

1. First, calculate the number of days in a year using ordinary interest, which is 360 days.
2. Next, calculate the interest: Interest = Principal × Rate × Time
3. Here, Time = 90/360, as the loan is for 90 days.
4. So, Interest = $1,300,000 × 0.14 × (90/360) = $45,500.

b.) Interest using exact interest at 14% on the same loan:

1. This time, use 365 days for exact interest calculations.
2. Interest = $1,300,000 × 0.14 × (90/365) = $44,246.58.

c.) Interest using ordinary interest at the reduced rate of 13.5%:

1. Interest = $1,300,000 × 0.135 × (90/360) = $43,312.50.

d.) To compete with Rimrock Bank's offer, Southside National Bank needs to decrease their interest by $1,875 from Rimrock's offer of $43,312.50, which would be an interest amount of $41,437.50.

To find the new rate for Southside National Bank:

1. First, we use the exact interest formula: Interest = Principal × Rate × Time.
2. Here, we want to find the Rate, so Rate = Interest / (Principal × Time)
3. Rate = $41,437.50 / ($1,300,000 × (90/365)) ≈ 0.1155 or 11.55%.