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
Hayden, a buyer for a medium-sized company, is assessing the value of competing software products for use in his firm. Which of
sveta [45]

Answer: A. Speech of delivery

Explanation:

When buying things like software, there are certain things that will determine the value apart from the monetary price. These include the ease of installation and the availability of training assistance.

With ease of installation, the fundamental question is if the software is easy or complicated to install. The easier it is the better. Also is there someone who can help the users be able to master the features of the software. This is availability of training assistance.

Now while speech of delivery can help in convincing Hayden to buy from a particular shop, it does not contribute to the value of the software.

6 0
3 years ago
What is the similar about negative growth rate and zero growth rate?
kifflom [539]
The similarity of negative growth rate and zero growth rate is that there is no growth towards a positive output. For example, if the business is currently in either state, it is not earning. It may be very stagnant (for zero growth rate) or losing (for negative growth rate). Which either the case may be, it is not beneficial to the business owner. 
3 0
3 years ago
Read 2 more answers
ROM Corporation had kept all its hiring plans on hold during the last four quarters because the economy was in a state of recess
Vanyuwa [196]

Answer:

D. Computer manufacturers have aggressively started hiring more staff

Explanation:

8 0
3 years ago
Suppose that you deposit $4,500 in your bank and the required reserve ratio is 18 percent. the maximum loan your bank can make a
NNADVOKAT [17]

Suppose that you deposit $4,500 in your bank and the required reserve ratio is 18 percent. The maximum loan your bank can make as a direct result of your deposit is 3690.

<h3>What exactly is a bank loan and the required reserve ratio?</h3>
  • A loan is a quantity of money that one or more people or businesses obtain from banks or other financial organizations in order to handle their finances in connection with anticipated or unforeseen circumstances.
  • By doing this, the borrower creates a debt that must be repaid with interest within a predetermined time frame.
  • The percentage of deposits that authorities mandate a bank maintain in reserves and refrain from lending out is known as the required reserve ratio.
  • If the required reserve ratio is 1 to 10, a bank can only lend out $0.90 of every dollar it has on deposit, but it must retain $0.10 in reserves.

Hence, The maximum loan your bank can make as a direct result of your deposit is 3690.

To learn more about the loan, refer to the following link:

brainly.com/question/25599836

#SPJ4

6 0
1 year ago
When a person whose duty is conditional leads the other party to rely on his noninsistence on the condition, the condition will
Tems11 [23]
The condition will be excused because of ESTOPPEL. Estoppel is an obstruction which prevents a person from asserting a right or denying a fact. The obstruction is normally due to the person action, conduct or failure to act. The principal aim of estoppel is to prevent injustice due to inconsistency or fraud. Estoppel is of two types: equitable and legal estoppel. 
3 0
2 years ago
Other questions:
  • According to the leadership grid developed by Blake and Mouton, which management style reflects moderate concern for production
    11·1 answer
  • On January 1, Year 5, customers owed Eagle $40,000. On December 31, Year 5, customers owed Eagle $30,000. Eagle uses the direct
    5·1 answer
  • Marlee mills owns a home in the village of Sheridan with a market value of $46,800. The assessed value of the home is $16,380. A
    11·1 answer
  • Consumers might not realize that old spice health and wellness products and iams pet nutrition products are made by the same com
    15·1 answer
  • Which of the following would you add to the balance per general ledger to arrive at the reconciled cash balance in a bank reconc
    11·1 answer
  • In which ways can goals be classified
    12·1 answer
  • What is the most important function of a leader within an organization?
    5·2 answers
  • In 1945, an African American family tries to purchase a home in a White neighborhood, but realtors and mortgage lenders refused
    12·1 answer
  • Madsen Motors's bonds have 18 years remaining to maturity. Interest is paid annually, they have a $1,000 par value, the coupon i
    7·1 answer
  • A sample of 40 individuals at a shopping mall found that the mean number of visits to a restaurant per week was 2.88 with a stan
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!