500 + b = 200. What would b equal?
1 answer:
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Answer:
The compounded annually account will earn more interest over 10 years
Step-by-step explanation:
The rule of the simple interest is I = Prt, where
- P is the original value
- r is the rate in decimal
- t is the time
The rule of the compounded interest is A = P, where
- A is the new value
- P is the original value
- r is the rate in decimal
- n is the number of periods
- t is the time
The interest I = A - P
∵ Each account start with $200
∴ P = 200
∵ They have an interest rate of 5%
∴ r = 5% = 5 ÷ 100 = 0.05
∵ One account earns simple interest and the other is compounded
annually
∴ n = 1 ⇒ compounded annually
∵ The time is 10 years
∴ t = 10
→ Substitute these values in the two rules above
∵ I = 200(0.05)(10)
∴ I = 100
∴ The simple interest = $100
∵ I = A - P
∵ A = 200
∴ A = 325.7789254
∵ I = 325.7789254 - 200
∴ I = 125.7789254
∴ The compounded interest = $125.7789254
∵ The simple interest is $100
∵ The compounded interest is $125.7789254
∵ $125.7789254 > $100
∴ The compounded annually account will earn more interest
over 10 years
Answer:
The mathematical expectation of a student who purchases 10 tickets is -$39.65.
Step-by-step explanation:
A student that purchases 10 tickets out of 2900 has a probability of winning the cruise that can be calculated as:
Each ticket cost $5, so he has spent $50 for the 10 tickets.
Then, the expected value of this operation is equal to the expected value of the earnings (probability of winning the prize multiplied by the value of the prize), minus the costs:
The mathematical expectation of a student who purchases 10 tickets is -$39.65.