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
Alex787 [66]
3 years ago
11

You have $36,948.61 in a brokerage account, and you plan to deposit an additional $3,000 at the end of every future year until y

our account totals $280,000. you expect to earn 11% annually on the account. how many years will it take to reach your goal? round your answer to two decimal places at the end of the calculations.
Mathematics
1 answer:
Luba_88 [7]3 years ago
8 0
Current amount in account
P=36948.61

Future value of this amount after n years at i=11% annual interest
F1=P(1+i)^n
=36948.61(1.11)^n

Future value of $3000 annual deposits after n years at i=11%
F2=A((1+i)^n-1)/i
=3000(1.11^n-1)/0.11

We'd like to have F1+F2=280000, so forming following equation:
F1+F2=280000
=>
36948.61(1.11)^n+3000(1.11^n-1)/0.11=280000

We can solve this by trial and error.


The rule of 72 tells us that money at 11% deposited will double in 72/11=6.5 years, approximately.
The initial amount of 36948.61 will become 4 times as much in 13 years, equal to approximately 147800 by then.
Meanwhile the 3000 a year for 13 years has a total of 39000.  It will only grow about half as fast, namely doubling in about 13 years, or worth 78000.
Future value at 13 years = 147800+78000=225800.
That will take approximately 2 more years, or 225800*1.11^2=278000.

So our first guess is 15 years, and calculate the target amount
=36948.61(1.11)^15+3000(1.11^15-1)/0.11
=280000.01, right on.

So it takes 15.00 years to reach the goal of 280000 years.
You might be interested in
8 1/2 - 6 1/4 please subtract
Alexandra [31]

Answer:

2.25

Step-by-step explanation:

8.5-6.25

(8-6)+(0.5-0.25)

2+0.25

2.25

4 0
3 years ago
Read 2 more answers
Help me please it's a quiz
lesya692 [45]

Answer:

8000in³

Step-by-step explanation:

20³=20*20*20=8000

7 0
2 years ago
What does 6/2(1+2)= <br> need help
Zina [86]

▪ Answer:

9

▪ Step-by-step explanation:

Hi there !

6/2(1 + 2) =

= 3/1 × 3

= 3×3/1

= 9

Good luck !

7 0
3 years ago
Read 2 more answers
Given f(x) = 3x+4 . What is f(8)
DerKrebs [107]
If x=8 {f(8)=3x+4}, the answer is 28.


Comment the correct answer. 
7 0
3 years ago
Read 2 more answers
Which statements are true? *<br> 1:2 = 50:100<br> 2:1 = 50:100<br> 1:2 = 2:1<br> 3:4 = 9:12
Bumek [7]
1:2 = 2:1 is the statement
6 0
3 years ago
Other questions:
  • Suppose you go shopping for a new futon bed for your apartment/home. The model you really like happens to be on sale for $1100.
    6·1 answer
  • A hippopotamus can run at the speed of about 24.9 miles per hour. At this rate, how far can the hippo run in 30 minutes? Use the
    8·2 answers
  • Find the 102nd term,given the first term and the common difference <br><br> A1=52 and d=12
    6·1 answer
  • Simplify (0.4) to the third power
    8·2 answers
  • the price of a DVD is $19 this price is 12% lower than last week what was the price of the DVD last week round your answer to th
    12·1 answer
  • A building has two sizes of apartments Smart in regular the ratio of small apartments to regular apartments is 18 to 7 what perc
    9·1 answer
  • Myles doesn't want to spend more than $11,000 per month on gate keepers. He hires 12 gate keepers who work an
    14·1 answer
  • What is the area of the circle. Explain your work.
    15·1 answer
  • An unknown number is not equal to 3.6 but rounds to 3.6 when rounded to the nearest tenth, what could be the number?
    7·1 answer
  • Which decimal is equivalent to<br> NI<br> OA) 0.416<br> B) 0.416<br> C) 0.416<br> OD) 0.416
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!