## 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

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**