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
Lelu [443]
3 years ago
6

On 1st January 2020, Laurie invests P dollars in an account that pays a nominal annual interest rate of 5.5%, compounded quarter

ly. The amount of money in Laurie’s account at the end of each year follows a geometric sequence with a common ratio, r. Find the value of r. Also, Laurie makes no further deposits to or withdrawals from the account. Find the year in which the amount of money in Laurie’s account will become double the amount she invested.
Mathematics
1 answer:
andrezito [222]3 years ago
3 0

Answer:

1) The common ratio =  1.055

2) The year in which the amount of money in Laurie's account will become double is the year 2032

Step-by-step explanation:

1) The given information are;

The date Laurie made the investment = 1st, January, 2020

The annual interest rate of the investment = 5.5%

Type of interest rate = Compound interest

Therefore, we have;

The value, amount, of the investment after a given number of year, given as follows;

Amount in her account = a, a × (1 + i), a × (1 + i)², a × (1 + i)³, a × (1 + i)ⁿ

Which is in the form of the sum of a geometric progression, Sₙ given as follows;

Sₙ = a + a × r + a × r² + a × r³ + ... + a × rⁿ

Where;

n = The number of years

Therefore, the common ratio = 1 + i = r = 1 + 0.055 = 1.055

The common ratio =  1.055

2) When the money doubles, we have;

2·a = a × rⁿ = a × 1.055ⁿ

2·a = a × 1.055ⁿ

2·a/a = 2 = 1.055ⁿ

2 = 1.055ⁿ

Taking log of both sides gives;

㏒2 = ㏒(1.055ⁿ) = n × ㏒(1.055)

㏒2 = n × ㏒(1.055)

n = ㏒2/(㏒(1.055)) ≈ 12.95

The number of years it will take for the amount of money in Laurie's account to double = n = 12.95 years

Therefore, the year in which the amount of money in Laurie's account will become double = 2020 + 12..95 = 2032.95 which is the year 2032

The year in which the amount of money in Laurie's account will become double = year 2032.

You might be interested in
Help it’s for my final most of my grade
Cloud [144]
-11.3 so the answer is B
4 0
2 years ago
Find the slope of the line passing through (3, -7) and (-1, 1). *
Svet_ta [14]

Answer:

-1/2.

Step-by-step explanation:

Slope = rise / run

= (1 - -7) / (-1 -3)

= 8/-4

= -1/2.

4 0
3 years ago
Read 2 more answers
What is y in 15=-7.5x^2+86x+702
dexar [7]

Answer:

  • add 15<em>x</em><em> </em><em>a</em><em>n</em><em>d</em><em> </em><em>8</em><em>6</em><em>x</em><em> </em><em>e</em><em>q</em><em>u</em><em>a</em><em>l</em><em> </em><em>t</em><em>o</em><em> </em><em>7</em><em>1</em><em>x</em>
8 0
3 years ago
Square root of x equals ten
Gala2k [10]
The square root of x equals ten is 5
8 0
3 years ago
The value of y varies directly with x. If x=4, then y=10. a. Find the constant of proportionality. b. Write an equation to repre
Lynna [10]

Answer:

aaaa

Step-by-step explanation:

In a short paragraph, describe how you would determine the amount of work needed to pull a toboggan the length of a football field. Be sure to include the equipment list and describe the measurements that you will take.

3 0
3 years ago
Other questions:
  • 32(6x + 4) find the value for x
    7·2 answers
  • ❤️❤️help would be appreciated
    13·1 answer
  • Let f(x) = |x|, ????????(x) = f(x − 3), and h(x) = f(x + 2), where x can be any real number.
    11·1 answer
  • The length of a string in yards is a function f(n) of the length n in inches. Write a function rule for this situation.
    5·1 answer
  • Twenty of the 25 students in Mrs. Thigpen’s class are we wearing sneakers. What is the fraction in simplest form?
    11·1 answer
  • HURRY JUST GIVE THE ANSWER PLZ!!
    13·2 answers
  • What is the value of x in the equation -5/4x=-160
    9·2 answers
  • Can anyone answer this ?
    6·1 answer
  • HELPPPPPPP<br> I HAVE 20 MINUTES
    9·1 answer
  • the value ax^2 + bx is 5 when x=1, and is equal to 0 when x=1.what are the values of a and b. explain how u arrived at your answ
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!