1.FIND the bank discount and proceeds on the following loans

i) RM4000 FOR 3 MONTHS at 10 1/2 percent

ii) RM4215 FROM 10 june to 5 august of the same year at 10 percent

To find the bank discount and proceeds for the given loans, we need to use the formulas for bank discount and proceeds.

The formula for calculating the bank discount (BD) is:
BD = Face Value * Rate * Time

The formula for calculating the proceeds (P) is:
P = Face Value - BD

Now, let's calculate the bank discount and proceeds for each loan:

i) Loan: RM4000 for 3 months at 10 1/2 percent
Face Value (FV) = RM4000
Rate (R) = 10 1/2% = 10.5%
Time (T) = 3 months = 3/12 years

Step 1: Calculate the bank discount (BD):
BD = FV * R * T
BD = 4000 * (10.5/100) * (3/12)
BD = 140 * 0.875
BD = RM122.50

Step 2: Calculate the proceeds (P):
P = FV - BD
P = 4000 - 122.50
P = RM3877.50

Therefore, the bank discount is RM122.50, and the proceeds on the loan are RM3877.50.

ii) Loan: RM4215 from 10 June to 5 August of the same year at 10 percent
Face Value (FV) = RM4215
Rate (R) = 10%
Time (T) = 5 August - 10 June = 1 month = 1/12 years

Step 1: Calculate the bank discount (BD):
BD = FV * R * T
BD = 4215 * (10/100) * (1/12)
BD = 4215 * (0.10/12)
BD = 35.125

Step 2: Calculate the proceeds (P):
P = FV - BD
P = 4215 - 35.125
P = RM4180.875

Therefore, the bank discount is RM35.125, and the proceeds on the loan are RM4180.875.

Note: In practical scenarios, the bank discount is usually rounded to two decimal places.