Questions

Okay, let's break down these two financial problems and solve them using Excel formulas. I'll provide the formulas and then explain how to use them in Excel.

Problem 1: Computer Purchase

1. Calculate the Initial Installment:

• Initial installment percentage: 40%
• Computer worth: $6,000,000
• Initial installment amount = 40% * $6,000,000 = $2,400,000

2. Calculate the Remaining Debt:

• Remaining debt = Computer worth - Initial installment amount
• Remaining debt = $6,000,000 - $2,400,000 = $3,600,000

3. Calculate the Monthly Installment using the PMT Function:

• Rate (interest rate per period): 3.5% effective monthly = 0.035
• Nper (total number of payment periods): 36 monthly installments = 36
• Pv (present value or principal of the loan): The remaining debt = $3,600,000
• Fv (future value, or a cash balance you want after the last payment): 0 (we want to pay off the entire debt)
• Type (when payments are due - 0 for end of period, 1 for beginning of period): 0 (assuming payments are made at the end of each month)

Excel Formula for Monthly Installment (Cell A1):

=PMT(0.035, 36, 3600000, 0, 0)

Explanation of the Formula:

• =PMT(): This is the Excel function for calculating the payment for a loan based on constant payments and a constant interest rate.
• 0.035: This is the monthly interest rate (3.5%).
• 36: This is the total number of payment periods (36 months).
• 3600000: This is the present value (the amount of the loan, $3,600,000).
• 0: This is the future value (0 because we want the loan to be fully paid).
• 0: This indicates that payments are due at the end of the period.

The result of this formula will be the monthly installment amount.

Problem 2: Debt Payoff with Biweekly Payments

1. Determine the Interest Rate per Biweekly Period:

• Annual interest rate: 24% convertible every 15 days. This means the nominal annual rate is 24%, and it's compounded biweekly.
• Number of biweekly periods in a year: 52 weeks / 2 weeks/period = 26 periods
• Interest rate per biweekly period = Annual rate / Number of periods
• Interest rate per biweekly period = 24% / 26 = 0.24 / 26 ≈ 0.00923077

2. Calculate the Number of Biweekly Payments using the NPER Function:

• Rate (interest rate per period): Approximately 0.00923077 (calculated above)
• Pmt (payment made each period): $391,250
• Pv (present value or principal of the loan): $8,500,000
• Fv (future value, or a cash balance you want after the last payment): 0 (we want to pay off the entire debt)
• Type (when payments are due - 0 for end of period, 1 for beginning of period): 0 (assuming payments are made at the end of the period)

Excel Formula for Number of Biweekly Payments (Cell B1):

=NPER(0.24/26, -391250, 8500000, 0, 0)

Explanation of the Formula:

• =NPER(): This is the Excel function for calculating the number of periods for a loan or investment based on constant payments and a constant interest rate.
• 0.24/26: This is the interest rate per biweekly period (annual rate divided by the number of biweekly periods).
• -391250: This is the payment made each biweekly period. It's entered as a negative value because it's money going out.
• 8500000: This is the present value (the initial debt of $8,500,000).
• 0: This is the future value (0 because we want the debt to be fully paid).
• 0: This indicates that payments are due at the end of the period.

The result of this formula will be the number of biweekly payments required to pay off the debt.

How to Use in Excel:

1. Open Microsoft Excel.

2. For Problem 1:

   • In cell A1, type the formula: =PMT(0.035, 36, 3600000, 0, 0)
   • Press Enter. The value displayed in cell A1 will be the monthly installment amount.

3. For Problem 2:

   • In cell B1, type the formula: =NPER(0.24/26, -391250, 8500000, 0, 0)
   • Press Enter. The value displayed in cell B1 will be the number of biweekly payments required.

By using these Excel formulas, you can easily calculate the required installment and the number of payments for each scenario. Remember to interpret the results in the context of the problem. The monthly installment for the computer purchase will be a negative value (as it's a payment), and the number of biweekly payments will be a positive number.