1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
algol13
3 years ago
11

Determine the time necessary for p dollars to double when it is invested at interest rate r compounded annually, monthly, daily,

and continuously. (round your answers to two decimal places.) r = 11%
Business
1 answer:
zvonat [6]3 years ago
8 0
<span>Annual = Years = 6.64; Actually 7 years Monthly = Years = 6.33; 6 Years, 4 months Daily = Years = 6.30; 6 Years, 111 days Continuously = 6.30; 6 Years, 110 days The formula for compound interest is FV = P*(1 + R/n)^(nt) where FV = Future Value P = Principle R = Annual interest rate n = number of periods per year t = number of years For this problem, we can ignore p and concentrate on the (1+R/n)^(nt) term, looking for where it becomes 2. So let's use this simplified formula: 2 = (1 + R/n)^(nt) With R, n, and t having the same meaning as in the original formula. For for the case of compounding annually 2 = (1 + R/n)^(nt) 2 = (1 + 0.11/1)^(1t) 2 = (1.11)^t The above equation is effectively asking for the logarithm of 2 using a base of 1.11. To do this take the log of 2 and divide by the log of 1.11. So log(2) / log(1.11) = 0.301029996 / 0.045322979 = 6.641884618 This explanation of creating logarithms to arbitrary bases will not be repeated for the other problems. The value of 6.641884618 indicates that many periods is needed. 6 is too low giving an increase of 1.11^6 =1.870414552 and 7 is too high, giving an increase of 1.11^7 = 2.076160153 But for the purpose of this problem, I'll say you double your money after 7 years. For compounding monthly: 2 = (1 + R/n)^(nt) 2 = (1 + 0.11/12)^(12t) 2 = (1 + 0.009166667)^(12t) 2 = 1.009166667^(12t) log(2)/log(1.009166667) = 0.301029996 / 0.003962897 = 75.96210258 And since the logarithm is actually 12*t, divide by 12 75.96210258 / 12 = 6.330175215 Which is 6 years and 4 months. For compounding daily: 2 = (1 + 0.11/365)^(365t) 2 = (1 + 0.00030137)^(365t) 2 = 1.00030137^(365t) log(2)/log(1.00030137) = 0.301029996 / 0.000130864 = 2300.334928 2300.334928 / 365 = 6.302287474 Continuously: For continuous compounding, there's a bit of calculus required and the final formula is FV = Pe^(rt) where FV = Future value P = Principle e = mathematical constant e. Approximately 2.718281828 r = Interest rate t = time in years Just as before, we'll simplify the formula and use 2 = e^(rt) Since we have the function ln(x) which is the natural log of x, I won't bother doing log conversions. rt = ln(2) 0.11 * t = 0.693147181 t = 0.693147181 / 0.11 t = 6.301338005</span>
You might be interested in
Help with economics?
umka2103 [35]
Changes in commodity prices
3 0
2 years ago
Minor company installs a machine in its factory at the beginning of the year at a cost of $135,000. the machine's useful life is
sveticcg [70]

To determine what the depreciation of an asset using straight line method, the formula to be used is:

(Initial cost of machine – salvage value) divided by estimated useful life


So in this problem:

Initial Cost - $135000

Salvage Value – $15000

Estimated Useful Life – 5 years

Plug that in the formula


Annual depreciation = ($135000 - $15000) / 5

= $120000/ 5

= $24,000


The first year depreciation for the machine is $24000 because the company bought it in the beginning of the year. (So there is no need to divide this by 12 months)

To record this:

Depreciation Expense $24000

<span>          Accumulated Depreciation $24000</span>

3 0
3 years ago
After an unsuccessful attempt to train her puppy one morning, Sharon, the office manager, scolds her assistant when she arrives
Assoli18 [71]
Displacement is the defense mechanism. Devised by the Freud's daughter Anna Frued which is one delicate follower of the Psychoanalysis theory and therapy pionnered by Sigmund himself. Defense mechanisms are told to be formed when there is a presence of anxiety, these anxieties are shaped when the id, ego and superego contradicts and coerces with one another. Thus defense mechanisms are formed to help the indivdual cope with his/her situation and anxiety. One is displacement as displayed in the statement above.
5 0
2 years ago
how much would be in your savings account in 9 years after depositing $160 today if the bank pays 9 percent per year
levacccp [35]

In 9 years after depositing $160, in my savings account would be $289.6

The formula for simple interest and procedure we will use to solve this exercise is:

S.I.= (P*R*T)/100

Where:

  • P = principal
  • R = rate of interest in % per annum
  • T = time

Information about the problem:

  • P = $160
  • R = 9%
  • T = 9 years
  • Total amount = ?

Applying the simple interest formula, we get:

S.I.= (P*R*T)/100

S.I.= (160* 9*9)/100

S.I.= $129.6

Calculating the total amount that would be in my savings account, we get:

Total amount = P + S.I.

Total amount = $160 + $129.6

Total amount = $289.6

<h3>What is simple interest?</h3>

It is the operation in which we calculate the profit produced by a capital loaned at a given percentage.

Learn more about simple interest at: brainly.com/question/20690803

#SPJ4

7 0
1 year ago
MC Qu. 107 The following information is available... The following information is available for a company's utility cost for ope
lianna [129]

Answer:

Variable cost Per Unit $2.50

Explanation:

Total cost at high activity = $8100

Total Cost at Low activity = $3600

Total Units at high activity = 2400

Total Units at low Activity = 600

Variable Cost Per Unit =  (High activity total Cost - Low activity total cost ) / (High Activity unit - low activity units)

Variable cost per unit = ($8100 - $3600) / (2400 - 600) = $4500 / 1800 = $2.50

7 0
3 years ago
Other questions:
  • A stock has an expected return of 14.3 percent, the risk-free rate is 3.9 percent, and the market risk premium is 7.8 percent. w
    12·2 answers
  • The concept "efficiency" has quite different meanings for economists (money out/money in), biologists (energy out/energy in), an
    7·1 answer
  • True or False: When economic profit is zero, producers do not have any incentive to deviate from the current line of production.
    5·1 answer
  • If you took a new, strong antibiotic, which vitamin would you most likely need that you didn't need before
    9·1 answer
  • Population of household composition, price of real estate in the area, availability of mortgage credit, consumer tastes, and inc
    14·1 answer
  • The brothers who created The GFB early on began shopping the product to independent coffee shops and then expanded into grocery
    11·1 answer
  • A company uses proprietary computer software to offer services that other companies have not been able to emulate. These service
    12·1 answer
  • JPix management is considering a stock split. JPix currently sells for $70 per share and a 3-for-1 stock split is contemplated.
    9·1 answer
  • Between 2000 and​ 2020, the U.S. government budget deficit
    8·1 answer
  • You are evaluating a potential purchase of several light-duty trucks. The initial cost of the trucks will be $194,000. The truck
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!