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 formulas used in bank discount calculations.
1. Bank Discount (BD):
Bank Discount is the interest charged by the bank for lending money before the maturity date. It is calculated using the formula:
BD = Principal × Rate × Time
Where:
- Principal is the initial amount of the loan.
- Rate is the annual interest rate expressed as a decimal.
- Time is the time period of the loan in years.
2. Proceeds:
Proceeds are the amount that the borrower receives after deducting the bank discount from the principal. It is calculated using the formula:
Proceeds = Principal - Bank Discount
Now, let's calculate the bank discount and proceeds for each loan:
i) Loan: RM4000 for 3 months at 10 1/2 percent
Principal (P) = RM4000
Rate (R) = 10.5% = 0.105 (since it is expressed as a decimal)
Time (T) = 3/12 year (3 months = 1/4 year)
Bank Discount (BD) = P × R × T
= RM4000 × 0.105 × (3/12)
= RM4000 × 0.105 × 0.25
= RM105
Proceeds = P - BD
= RM4000 - RM105
= RM3895
Therefore, the bank discount is RM105, and the proceeds are RM3895 for a loan of RM4000 for 3 months at 10 1/2 percent.
ii) Loan: RM4215 from 10 June to 5 August of the same year at 10 percent
Principal (P) = RM4215
Rate (R) = 10% = 0.10
Time (T) = 1 month + 25 days (from 10 June to 5 August)
To calculate the time in years, we need to convert months and days to fractions of a year.
1 month = 1/12 year
25 days = 25/365 year (assuming a 365-day year)
Time (T) = (1/12) + (25/365)
Bank Discount (BD) = P × R × T
= RM4215 × 0.10 × [(1/12) + (25/365)]
= RM4215 × 0.10 × (0.083 + 0.0685)
= RM4215 × 0.10 × 0.1515
= RM63.9375
Proceeds = P - BD
= RM4215 - RM63.9375
= RM4151.0625 (rounded to RM4151.06)
Therefore, the bank discount is RM63.94, and the proceeds are RM4151.06 for a loan of RM4215 from 10 June to 5 August of the same year at 10 percent.