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
Lady_Fox [76]
3 years ago
11

18. If you have $1,000 to deposit in a savings account for 1 year, which of the following should you choose: 8.75% compounded co

ntinuously, 9% compounded quarterly, or 9.5% compounded annually. a) 8.75% compounded continuously d) a and b are equivalent and are best. b) 9% compounded quarterly e) a, b and c are all exactly equivalent. c) 9.5% compounded annually
Business
2 answers:
sladkih [1.3K]3 years ago
7 0

Answer:

c) 9.5% compounded annually

Explanation:

effective rate for a)

e^{0.0875}=1+r\\

1.091442264 = 1+r

r = 0.09144= 9.14%

effective rate for b)

(1+0.09/4)^4 = 1+r_e

1.093083319 = 1+ re

re = 0.0931 = 9.31%

effective rate for c)

as it comounds annuity it is the effective rate already 9.5%

As we are capitalizing the interest we want the higher rate thus 9.5 percent compounding annually

Whitepunk [10]3 years ago
5 0

Answer: 9.5% compounded annually (option c)

Explanation:

Formula for calculating continuous compounding:

Fv = Pv × [(e)^(i × t)]

Where Fv = future value

Pv = present value

e = mathematical constant approximated as 2.7183

Now, in the first case ---- 8.75% compounded continuously

Fv = Pv × [(e)^(i × t)]

Here "Pv" is $1,000. "i" is 0.0875 (divide 8.75 by 100) and "t" is 1

Therefore Fv = 1000 × (2.7183)^(0.0875 × 1)

= 1000 × [(2.7183)^(0.0875)]

= 1000 × 1.091443

= $ 1091.44

Subtracting $1000 from $1091.44:

1091.44 - 1000

This means that I will gain $91.44 over this period (1 year).

If it was 9% compounded quarterly:-

We apply the formula

Fv = Pv × [1 + (i/n)^(n×t)]

Where Pv = present value of investment

i = stated interest rate

n = number of compounding periods

t = time in years

Here, Pv is $1,000. "i" is 9% or 0.09, "t" is 1year and "n" is 4(since it will be compounded quarterly).

Fv = 1000 × [1 + (0.09/4)^(4×1)]

= 1000 × [(1.0225)^4]

= $1,093.08

Subtracting the pv from 1,093.08 it is clear that I'll gain $93.08 over this period

For 9.5% compounded annually (n is 1 in this case):

Fv = 1000 × [1 + ((0.095/1)^(1×1)]

= 1000 × [(1.095)^1]

= $1,095

Subtracting the Pv from the Fv, it shows that I'll gain $95 if it's compounded this way over the same period.

Since I will always prefer the system that can yield the most return, it's only logical that I go for option c (9.5% compounded annually)

You might be interested in
Interest rates on 3-year Treasury securities are currently 1.92%, while 10-year Treasury securities yield 5.62%. If the pure exp
FromTheMoon [43]

Answer: 7.24%

Explanation:

From the question, we are told that:

3 years treasury securities have an interest rate = 1.92%

10 years treasury security has an interest rate = 5.62%

Let the 7 year treasury security interest in 3 years be represented by z.

Based on the expectation theory

( 1+1.92%)^3 × (1 + z%)^7 = (1 + 5.62%)^10

(1+0.0192)^3 × (1 + z%)^7 = (1 + 0.0562)^10

(1.0192)^3 (1 + z%)^7 = (1.0562)^10

1.05871(1 + z%)^7 = 1.72767

Divide both side by 1.05871

(1 + z%)^7 = 1.72767/1.05871

(1 + z%)^7= 1.6319

1 + z% = 1.6319^1/7

1 + z% = 1.6319^0.1429

1 + z% = 1.0724

z% = 1.0724 - 1

z% = 0.0724

We then convert the decimal to percentage

z = 7.24%

The market believes that 7-year Treasury securities will be yielding 7.24% in 3 years .

3 0
3 years ago
9. The cost of producing one more unit of a good is known as a(n) (1) Fixed cost. (2) Variable cost. (3) Operating cost. (4) Mar
miskamm [114]

Answer:

Marginal cost.​

Explanation:

6 0
3 years ago
You're trying to save to buy a new $199,000 Ferrari. You have $49,000 today that can be invested at your bank. The bank pays 5.7
Gelneren [198K]

Answer:

It will take 25.28 year to have enough to buy the car ( ignoring Inflation effect)

Explanation:

Current Deposit = PV = $49,000

Future Value = FV = $199,000

Interest Rate = r = 5.7%

Use following Formula

FV = PV ( 1 + r )^n

$199,000 = $49,000 ( 1 + 0.057 )^n

$199,000 / $49,000 = ( 1 + 0.057 )^n

4.06 = 1.057^n

Log 4.06 = n log 1.057

n = log 4.06 / log 1.057

n = 25.28

it requires 25.28 year to have an amount to buy the Ferrari.

6 0
3 years ago
All of the following are determinants of demand elasticity EXCEPT a. whether the purchase of the product can be delayed b. wheth
yKpoI14uk [10]

Answer:

The correct answer is option d. whether the product has utility.

Explanation:

The demand elasticity is a concept that explains the elasticity of the consumer in terms of buying a product while its price rises.

All of the factors given in the question are a part of this concept except whether the product has utility.

The reason is that when a consumer buys something, the utility of that desire is not measured. If people have a high demand elasticity, they would buy the most priciest of things which have no utility  as such.

3 0
2 years ago
Which principle of design is used to make one element of a design stand out?
Olegator [25]
B is the correct answer.
5 0
3 years ago
Read 2 more answers
Other questions:
  • ____ evaluation methods use some measurable quantity as the basis for assessing performance.
    10·1 answer
  • Bunny Bread Company manufactures different types of bread and accounts for its production using an ABC costing system. It has a
    12·1 answer
  • The Roland Company needs to comply with the financial reporting standards of the Sarbanes-Oxley Act. One of the employees, Ken,
    8·1 answer
  • Prepare an adjusted trial balance as of December 31. (Enter your answers in thousands of dollars.) MINT CLEANING INC. Adjusted T
    7·1 answer
  • Today you put $1000 in the bank. your bank pays 5% interest, continuously compounded. in 3 years, how much money will you have i
    11·1 answer
  • Carson Corporation stock sells for $35 per share, and you’ve decided to purchase as many shares as you possibly can. You have $5
    10·1 answer
  • What type of value may consumers be interested in if they are looking for the potential rate of return
    11·1 answer
  • Identify the correct statement. Group of answer choices An increase in the price level in an economy will decrease the real GDP
    11·1 answer
  • which of the following agencies manages and deploys the Integrated Ballistic Identification System A. FTI B. FBI C. ATF D. DOJ
    10·1 answer
  • How does Apple Inc. demonstrate the importance of the mission and vision to employees and stakeholders?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!