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When thinking about loans or investments, understanding interest compounding is important. Compounding means that the interest you earn or pay is calculated on both the initial principal and the accumulated interest from previous periods.

Daily compounding means this interest calculation happens every single day. Imagine you have a loan with daily compounding. Today, the interest is calculated on your entire balance. Tomorrow, it's calculated on your balance plus the tiny bit of interest added today. This might seem small, but over time, it makes a big difference.

The formula to find the Effective Annual Rate (EAR) with daily compounding is useful here:

• It shows how much you're truly paying or earning over a year.
• The EAR formula is: \[EAR = \left(1 + \frac{r}{n}\right)^n - 1\] where \(r\) is the nominal interest rate, and \(n\) is the number of compounding periods in a year (360 for daily compounding).

Using this formula helps make informed financial decisions by understanding the real cost of taking a loan or the actual returns on investments.

Credit terms define the conditions under which a business extends credit to a buyer. These terms dictate how long the buyer has to pay the due amount. For instance, in the exercise, the firm considers giving customers 90 days to pay.

Credit terms directly impact cash flow. By allowing customers to pay later, businesses might need to borrow to cover the liquidity gap temporarily. This is where the cost of credit comes into play. Offering credit for 90 days means the interested customers understand the time value of money, holding payments until the last day reduces their expenses.

To ensure the business remains stable when offering credit, understanding the equivalent interest costs and adjusting base prices might be necessary. This strategy ensures the company doesn't lose money due to extended credit terms.

Interest cost calculation is crucial when your business is considering credit options. Suppose you extended a 90-day credit to your customers and required a loan to manage your accounts. Then calculating how much the loan's interest affects your profits is key.

The interest rate for the 90-day period needs calculation. This requires knowing the effective interest rate for that duration:

• Use the formula \[(1 + \frac{r}{n})^t - 1\] where \(r\) is the annual nominal rate, \(n\) is the number of compounding periods (360 days), and \(t\) is the number of days (90 days in this example).
• This calculation gives the total interest cost for the 90-day period.

Converting this interest into a price increase percentage ensures you're covered against any financial loss due to late payments. Simply multiplying the obtained rate by 100 gives the percentage needed. Rounding this to the nearest whole number provides a clear, actionable figure for price adjustments.