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 on the given loans, we need to understand the terms involved. The bank discount is the amount deducted from the face value (the original loan amount) and represents the interest that the bank charges for the loan period. The proceeds refer to the amount received by the borrower after deducting the bank discount from the face value.
i) RM4000 FOR 3 MONTHS at 10 1/2 percent:
Step 1: Convert the interest rate to a decimal fraction by dividing it by 100.
Interest rate = 10 1/2 percent = 10.5% = 10.5/100 = 0.105
Step 2: Calculate the bank discount using the formula:
Bank Discount = Face Value × Interest Rate × Time
Bank Discount = RM4000 × 0.105 × (3/12) [Converting 3 months to years (3/12)]
Bank Discount = RM4000 × 0.105 × 0.25 [Simplifying the calculation]
Bank Discount = RM105
Step 3: Calculate the proceeds using the formula:
Proceeds = Face Value - Bank Discount
Proceeds = RM4000 - RM105
Proceeds = RM3895
For a loan of RM4000 for 3 months at 10 1/2 percent, the bank discount is RM105, and the proceeds are RM3895.
ii) RM4215 FROM 10 June to 5 August of the same year at 10 percent:
Step 1: Determine the number of days in the loan period.
From 10 June to 5 August = 2 months and 26 days
Step 2: Convert the interest rate to a decimal fraction.
Interest rate = 10% = 10/100 = 0.10
Step 3: Calculate the bank discount using the formula for exact interest:
Bank Discount = Face Value × Interest Rate × Time
Bank Discount = RM4215 × 0.10 × (2 + 26/365) [Converting 2 months and 26 days to years]
Bank Discount = RM4215 × 0.10 × (2.071) [Simplifying the calculation]
Bank Discount = RM868.33 (approximately)
Step 4: Calculate the proceeds using the formula:
Proceeds = Face Value - Bank Discount
Proceeds = RM4215 - RM868.33
Proceeds = RM3346.67 (approximately)
For a loan of RM4215 from 10 June to 5 August at 10 percent, the bank discount is approximately RM868.33, and the proceeds are approximately RM3346.67.