A man borrows money from a bank which uses a simple discount rate of 14%. He signs a promissory note promising to pay P500 per month at the end of the 4th, 6th and 7th months, respectively. Determine the amount he received from the bank.

Question

A man borrows money from a bank which uses a simple discount rate of 14%. He signs a promissory note promising to pay P500 per month at the end of the 4th, 6th and 7th months, respectively. Determine the amount he received from the bank.

Answer

Step 1: Calculate the present value of each payment.

We need to find the present value of each P500 payment considering the simple discount rate and the time remaining until the payment is due. Use the formula:

Present Value (PV) = Future Value (FV) / (1 + Rate * Time)

where:

  • FV: P500 (the face value of each payment)
  • Rate: 14% (annual discount rate)
  • Time: Number of months remaining until the payment is due
  • Present value of first payment (due in 4 months): PV1 = 500 / (1 + 0.14 * 4/12) ≈ P411.46
  • Present value of second payment (due in 6 months): PV2 = 500 / (1 + 0.14 * 6/12) ≈ P370.37
  • Present value of third payment (due in 7 months): PV3 = 500 / (1 + 0.14 * 7/12) ≈ P355.56

Step 2: Sum the present values of all payments.

The total amount the man received from the bank is the sum of the present values of all three payments:

Total Present Value (TPV) = PV1 + PV2 + PV3

TPV ≈ P411.46 + P370.37 + P355.56 ≈ P1137.39

Therefore, the man received approximately P1137.39 from the bank.

Note: This is an approximation due to rounding in the calculations. The actual amount received might be slightly different depending on the rounding method used.

OR

Promisory Note Pays P500 at the end of 4th, 6th and 7th months respectively

Calculatiing the Present Value of these Payments:-

where, AMount = P500

r = Simple discount rate = 14%

n1 = Payment in 4th month

n2 = Payment in 6th month

n3 = Payment in 7th month

A man borrows money from a bank which uses a simple discount rate of 14%. He signs a promissory note promising to pay P500 per month at the end of the 4th, 6th and 7th months, respectively. Determine the amount he received from the bank.

Present Value = P477.71 + P467.29 + $462.25

Present Value = P1407.25

So, the amount of money that he received from the bank is P1407.25

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