Question

On June 3, 2019, Paula obtains a loan from a bank to be repaid on December 3, 2019. If the bank charges 10.5% discount interest rate, what must be the face value of anon-interest-bearing note that will have proceeds of ₱250 000?

Answer 1

The face value of the non-interest-bearing note must be approximately ₱263,852.80 to ensure proceeds of ₱250,000 after the bank's 10.5% discount interest rate over 6 months.

Step-by-step explanation:

To calculate the face value of a non-interest-bearing note with proceeds of ₱250,000 and a discount rate of 10.5%, we use the formula for the present value of a single sum. We start by calculating the interest, which in this case is a discount taken from the face value of the note. The discount can be found using the formula Interest (Discount) = Principal × Rate × Time, where the rate is given as a decimal.

First, convert the months into years by dividing the number of months by 12. Since the loan period is from June 3, 2019, to December 3, 2019, that's 6 months or 0.5 years. Next, use the formula:

Face Value = Loan Amount / (1 - (Interest Rate × Time))

Plugging in the information we have:

Face Value = ₱250,000 / (1 - (0.105 × 0.5))

Face Value = ₱250,000 / (1 - 0.0525)

Face Value = ₱250,000 / 0.947

Face Value = ₱263,852.80

Thus, the face value of the note must be approximately ₱263,852.80 to ensure Paula receives the desired proceeds of ₱250,000 when accounting for the 10.5% discount interest rate over 6 months.