Suppose $250,000 is used to establish an annuity that earns 6%, compounded quarterly, and pays $6000 at the end of each quarter. It will take about 120 quarters until the account balance reaches $0.
Amount invested (Present value) = $250000
Quarterly payment (At the end of each quarter) (P) = $4500
Interest Rate (Quarterly) (r) = 6% /4
= 1.5% = 0.015
A number of quarters (n) = ?
Future value at the end = 0
Present value of Annuity formula:
Present value = P × ![(1-(1+r))^{(-n)} / r](https://tex.z-dn.net/?f=%281-%281%2Br%29%29%5E%7B%28-n%29%7D%20%20%2F%20r)
250000 = 4500 × ![(1-((1+0.015))^{(-n)} / 0.015](https://tex.z-dn.net/?f=%281-%28%281%2B0.015%29%29%5E%7B%28-n%29%7D%20%20%2F%200.015)
250000 = 300000 × ![(1-((1+0.015)}}^{(-n)}](https://tex.z-dn.net/?f=%281-%28%281%2B0.015%29%7D%7D%5E%7B%28-n%29%7D)
250000 / 300000 = ![1-(1+0.015)^{(-n)}](https://tex.z-dn.net/?f=1-%281%2B0.015%29%5E%7B%28-n%29%7D)
0.83333 = ![1-(1.015)^{(-n)](https://tex.z-dn.net/?f=1-%281.015%29%5E%7B%28-n%29)
n = 120
Hence is shall take 120 Quarters until the account balance is $0.
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Given the consumption equation of c= 200 + 0.85yd, and the disposable income of $400, then, then we would get the consumption by substituting the given to the equation:c= 200 + 0.85ydc= 200 + 0.85(400)c= 200 + 340c= 540Therefore, the consumption is $540.
Answer:
r= 3
Explanation:
Due that the level price does not changed, the first thing that you have to do to find the equilibrium is put the two equations with an equal
Money demand =Supply of money
2,200 – 200 r= 2,000
Now you have to find the value of r and you have to clear the formula and first you have to:
2,800- 2,200 = 200r
Now that you have the number together you have to apply the operation
600 = 200r
As the 200 is multiplying the r you have to pass the 200 to divided the 600
r= (600/200)
r= 3%
The interest rate is 3%
<span>a volcanic island forms and subsides</span>
Answer: A.
Explanation:
By definition, opportunity cost is the amount or value of something you gave up for another good.
For example: say you value sleeping in at $5 value going to class at $4. You decide to get up and go to class, the $4 value. Therefore, your opportunity cost is what you gave up (sleeping in) for another good/choice (going to class), is $5 since you valued sleeping in at that.