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
Mila [183]
1 year ago
6

NO LINKS!!! Kim invested $5000 in Mutual fund at 6% compounded quarterly. Write an equation to represent this situation. When wi

ll her investment be worth more than $10,000​
Mathematics
2 answers:
Ira Lisetskai [31]1 year ago
7 0

Answer:

Equation is  A = 5000(1.015)^(4t)

Her investment will be worth $10,000 in about <u>11.63888 years</u>

Rounding up to the nearest whole number gets to <u>12 years</u>

==========================================================

Explanation:

Part 1) Finding the equation

The compound interest formula is

A = P(1+r/n)^(n*t)

Here are the variables

  • A = final amount
  • P = starting amount, or deposit, or principal
  • r = interest rate in decimal form
  • n = number of times money is compounded per year
  • t = number of years

In this case,

  • P = 5000
  • r = 0.06 from the 6% annual interest
  • n = 4 times a year is the compounding frequency
  • t = unknown amount of time

Therefore, the equation is

A = P(1+r/n)^(n*t)

A = 5000(1+0.06/4)^(4t)

A = 5000(1.015)^(4t)

The decimal value is exact.

--------------------------

Part 2) Let's plug in A = 10,000 and solve for t.

You'll need to use logarithms to isolate the exponent.

A = 5000(1.015)^(4t)

10,000 = 5000(1.015)^(4t)

10,000/5000 = (1.015)^(4t)

2 = (1.015)^(4t)

Log[ 2 ] = Log[ (1.015)^(4t) ]

Log(2) = 4t*Log( 1.015 )

4t = Log(2)/Log(1.015)

4t = 46.5555256308062

t = 46.5555256308062/4

t = 11.6388814077015

t = 11.63888

It takes about 11.63888 years for the investment to reach $10,000.

Therefore, at the 12 year mark is when the investment is more than $10,000.

Yuki888 [10]1 year ago
4 0

Answer:

11 years and 9 months

Step-by-step explanation:

<u>Compound Interest Formula</u>

\large \text{$ \sf A=P(1+\frac{r}{n})^{nt} $}

where:

  • A = final amount
  • P = principal amount
  • r = interest rate (in decimal form)
  • n = number of times interest applied per time period
  • t = number of time periods elapsed

Given:

  • A = $10000
  • P = $5000
  • r = 6% = 0.06
  • n = 4 (as compounded quarterly)
  • t = years

Substitute the given values into the equation and solve for t:

\implies 10000=5000\left(1+\dfrac{0.06}{4}\right)^{4t}

\implies \dfrac{10000}{5000}=\left(1+0.015\right)^{4t}

\implies 2=\left(1.015\right)^{4t}

Take natural logs of both sides:

\implies \ln 2=\ln \left(1.015\right)^{4t}

Apply the power log law:

\implies \ln 2=4t\ln \left(1.015\right)

Simplify:

\implies t=\dfrac{\ln 2}{4 \ln 1.015}

\implies t=11.63888141

11.6388141... years ≈ 11 years and 7.7 months

As the interest is earned <u>quarterly</u>, round this to the nearest quarter

⇒ 11 years and 9 months.

Therefore, Kim's investment will be worth <em>more</em> than $10,000 at <u>11 years and 9 months</u>.

You might be interested in
Yesterday the Bandits scored 56 points in their basketball game. Today they scored 42 points. What is the percent decrease of Th
FromTheMoon [43]

Answer:

x = 25% percent decrease

Step-by-step explanation:

For this problem we will use percentage calculation and make proportion:

Initial value 56 points is worth 100%

Second value 56 - 42 = 14 points of decrease is worth x%

56 : 14 = 100 : x

When we multiply external and internal members we get:

56 · x = 14 · 100 => x = 1400/56 = 25%

x = 25% percent decrease

God with you!!!


5 0
2 years ago
Jan needed to empty 18 gallons of water from a tub into jugs that hold 0.5 gallons of water. How many jugs did Jan need?
Ilia_Sergeevich [38]
So you would do,
18 gallons of water divided by 0.5 gallons of water 
if you did that correctly you should have gotten... 36 jugs
8 0
3 years ago
Please Tell me what the answer
Helga [31]
OK for number 3is 70because you add the number that they give you and then subtract 36 106 and you get your answer


3 0
3 years ago
How do you go from slope-intercept form to standard form
dexar [7]
Thats How you go from slope to to standard form

6 0
3 years ago
Help please and thank you!
Usimov [2.4K]

Answer:

Option A

Explanation:

\rightarrow \sf sin\left(\dfrac{7\pi }{6}\right)

\rightarrow \sf \sin \left(\pi +\dfrac{\pi }{6}\right)

\rightarrow \sin \left(\pi \right)\cos \left(\dfrac{\pi }{6}\right)+\cos \left(\pi \right)\sin \left(\dfrac{\pi }{6}\right)

\rightarrow \sf 0 *  \dfrac{\sqrt{3}}{2}+\left(-1\right) * \dfrac{1}{2}

\rightarrow \sf -\dfrac{1}{2}

7 0
2 years ago
Other questions:
  • Answer this plzzzzzzz?
    9·2 answers
  • You need to cut a 9 foot piece of plywood into 12 inch sections. Every cut also removes 1/8 inch. How many 12 inch sections can
    5·1 answer
  • Fencing costs $3.25 per foot. A certain
    6·1 answer
  • I will give you a Brainly crown if it is right. Will you help me
    5·2 answers
  • THIS IS ONE OF THE HARDER QUESTIONS THAT I GOT ON MY TEST TY :)
    11·2 answers
  • Write the equation in slope-intercept form. -1.5(6y - 2x) = 0​
    13·1 answer
  • Please solve :)<br> 2y &lt; y + 2
    7·1 answer
  • Find two consecutive odd integers whose product is equal to 63​
    8·1 answer
  • Each table shows a proportional relationship between x and y, Match each table with its constant of proportionality
    12·1 answer
  • You used 3/8 of a tank of gas on a trip to the mountains and you used 1/6 of a tank of gas doing errands. You want to visit your
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!