find the discounted value of 500 due in 82 days at 9%, 1000 at 55 days at 15% using both ordinary and simplest interest?
Ordinary Interest
Ar = Ab - Ab*r*t.
Ar = 500 - 500*(0.09/360)*82 =
Amount received or Discounted value.
Ar = 1000 - 1000*(0.15/360)*55 =
Amount received or Discounted value.
To find the discounted value of the given amount due at a certain future date, we need to use the concept of present value. Present value is the value of a future sum of money in today's terms, taking into account the time value of money and any interest rates involved.
1. Ordinary Interest:
For ordinary interest, we need to find the simple interest on the given amounts.
- Discounted value of 500 due in 82 days at 9%:
Simple Interest = Principal * Rate * Time
Simple Interest = 500 * 9% * (82/365)
Simple Interest = 18.75
- Discounted value of 1000 due in 55 days at 15%:
Simple Interest = Principal * Rate * Time
Simple Interest = 1000 * 15% * (55/365)
Simple Interest = 20.55
2. Simple Interest:
For simple interest, we calculate the interest on the principal amount, then deduct it from the principal.
- Discounted value of 500 due in 82 days at 9%:
Simple Interest = Principal * Rate * Time
Simple Interest = 500 * 9% * (82/365)
Simple Interest = 18.75
Discounted Value = Principal - Simple Interest
Discounted Value = 500 - 18.75
Discounted Value = 481.25
- Discounted value of 1000 due in 55 days at 15%:
Simple Interest = Principal * Rate * Time
Simple Interest = 1000 * 15% * (55/365)
Simple Interest = 20.55
Discounted Value = Principal - Simple Interest
Discounted Value = 1000 - 20.55
Discounted Value = 979.45
In summary:
Ordinary Interest:
- Discounted value of 500 due in 82 days at 9%: $18.75
- Discounted value of 1000 due in 55 days at 15%: $20.55
Simple Interest:
- Discounted value of 500 due in 82 days at 9%: $481.25
- Discounted value of 1000 due in 55 days at 15%: $979.45