1.Joanne borrowed RM5000 for 180 days at a discount rateof 8 1/2 %.find the proceeds.
2.A businessman needs RM12000 for four months. What should be the size of the loan if his bank charges a discount rate of 9.5%.
1. To find the proceeds, we need to calculate the discount amount first.
Discount amount = loan amount * discount rate * time
Discount amount = RM5000 * 8.5% * (180/365) (assuming a 365-day year)
= RM5000 * 0.085 * 0.4931507
= RM209.22
The proceeds are the loan amount minus the discount amount.
Proceeds = loan amount - discount amount
Proceeds = RM5000 - RM209.22
= RM4790.78
Therefore, the proceeds are RM4790.78.
2. To find the size of the loan, we need to calculate the discount amount first.
Discount amount = desired amount * discount rate * time
Discount amount = RM12000 * 9.5% * (4/12) (assuming a 12-month year)
= RM12000 * 0.095 * 0.3333333
= RM380.00
The size of the loan is the desired amount plus the discount amount.
Size of loan = desired amount + discount amount
Size of loan = RM12000 + RM380.00
= RM12380.00
Therefore, the size of the loan should be RM12380.00.
To answer these questions and find the proceeds or the loan size, we need to understand the concept of discounting in finance.
Discounting is a calculation used to determine the future value of money at present. It is commonly used in financial transactions, such as loans and investments.
The formula for calculating the proceeds or loan size using discounting is as follows:
Proceeds = Principal * (1 - Discount Rate * Time)
Where:
- Proceeds: The amount received or the loan size
- Principal: The original amount borrowed or loaned
- Discount Rate: The rate at which the amount is discounted
- Time: The time duration for which the amount is discounted
Let's use this formula to solve the questions:
1. Joanne borrowed RM5000 for 180 days at a discount rate of 8 1/2 %.
First, we need to convert the discount rate to a decimal. 8 1/2 % can be written as 0.085.
Proceeds = RM5000 * (1 - 0.085 * (180/365))
Proceeds = RM5000 * (1 - 0.085 * 0.4932)
Proceeds = RM5000 * (1 - 0.0419)
Proceeds = RM5000 * 0.9581
Proceeds = RM4790.50
So, the proceeds are RM4790.50.
2. A businessman needs RM12000 for four months at a discount rate of 9.5%.
First, convert the discount rate to a decimal. 9.5% can be written as 0.095.
Loan Size = RM12000 * (1 - 0.095 * (4/12))
Loan Size = RM12000 * (1 - 0.095 * 0.3333)
Loan Size = RM12000 * (1 - 0.0317)
Loan Size = RM12000 * 0.9683
Loan Size = RM11619.60
So, the size of the loan should be RM11619.60.