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
Leni [432]
3 years ago
13

Seth has a bank account which pays 1.01% interest, compounded quarterly. Seth withdraws $4,567 from the account every quarter fo

r 35 years. Assuming that Seth does not make any deposits into this account and that the withdrawals occur at the end of every quarter, find the initial value of the account, rounded to the nearest cent.
a.

$765,824.68


b.

$767,758.39


c.

$538,021.66


d.

$539,380.16






Please select the best answer from the choices provided




A

B

C

D
Mathematics
2 answers:
dimulka [17.4K]3 years ago
6 0

Answer:

C. $538,021.66

Step-by-step explanation:

It is given that the money Seth withdraws was compounded every quarter for 35 years. So, we get,

Amount withdrawn every quarter, P = $4567

Rate of interest, r  = \frac{0.0101}{4} = 0.002525

Time period, n = 35 × 4 = 140

Now, as we know the formula for annuity as,

P=\frac{r \times PV}{1-(1+r)^{-n}}

where P = installments, PV = present value, r = rate of interest and n = time period.

This gives, PV=\frac{P \times [1-(1+r)^{-n}]}{r}

i.e. PV=\frac{4567 \times [1-(1+0.002525)^{-140}]}{0.002525}

i.e. PV=\frac{4567 \times [1-(1.002525)^{-140}]}{0.002525}

i.e. PV=\frac{4567 \times [1-0.7021]}{0.002525}

i.e. PV=\frac{4567 \times 0.2975}{0.002525}

i.e. PV=\frac{1358.68}{0.002525}

i.e. PV=538,091.08

So, the closest answer to initial value of the account is $538,021.66

Hence, option C is correct.

olganol [36]3 years ago
6 0
A=P \frac{1-(1+ \frac{r}{t} )^{-nt}}{ \frac{r}{t} }; where A is the initial value, P is the periodic withdrawal, r is the rate, t is the number of compounding in a year, n is the number of years.

A=P \frac{1-(1+ \frac{r}{t} )^{-nt}}{ \frac{r}{t} }  \\ =4,567 \times \frac{1-(1+ \frac{0.0101}{4} )^{-35 \times 4}}{ \frac{0.0101}{4} } \\ =4,567 \times \frac{1-(1+ 0.002525)^{-140}}{ 0.002525 } \\ =4,567 \times \frac{1-(1.002525)^{-140}}{ 0.002525 } \\ =4,567 \times \frac{1-0.7025}{ 0.002525 } \\ =4,567 \times \frac{0.2975}{ 0.002525 } \\ =4,567 \times 117.8 \\ =$538,021.66
Therefore, initial value = $538,021.66
You might be interested in
Ten more than 6 times a number is 4 less than 4 times the number. Please help me!!
Y_Kistochka [10]
10+6x=4x-4
6x-4x=-4-10
     2x=-14
      x-7
10=6(-7)=-32
4(-7)-4=-32
         =-32
6 0
3 years ago
The lighthouse was moved 230 feet inland at a rate of 40 feet per hour. How many hours did it take to move the lighthouse? What
Aleks04 [339]

Answer:

5.75

Step-by-step explanation:

4) 230 ÷ 40 = 5.75

3 0
3 years ago
What is the slope of the line that passes through the points
svetoff [14.1K]

Answer:

Step-by-step explanation:

6 0
3 years ago
Esma has a box that is 20 cm wide 10 cm high, and 10 cm deep she wants to fill the box with packages that are 5 cm wide 2 cm hig
anastassius [24]

Answer:

Esma can fit 3 packages in the box because 20+10+10=30 and 5+2+2=9 so if you add up 9 three times you get 27 and that is the closest number you can get before going over.

Step-by-step explanation:

6 0
2 years ago
What is the common difference, d, in the arithmetic sequence defined by the formula below? an=2n+1
marishachu [46]
<h3><u>Answer:</u></h3>

  • d = 2

<h3><u>Solution:</u></h3>

We are given that the arithmetic progression is defined by :

➝ 2n + 1

<em>Therefore, </em>

  • <u>For </u><u>first </u><u>term</u>

➙ n = 1

➝ 2 × 1 + 1

➝ 2 + 1

➝ 3

  • <u>For </u><u>second </u><u>term</u>

➙ n = 2

➝ 2 × 2 + 1

➝ 4 + 1

➝ 5

  • <u>Common </u><u>difference</u>

➙ 2nd term - 1st term

➝ 5 - 3

➝ 2

<h3><u>More </u><u>information</u><u>:</u></h3>

  • The difference between the successive term and the preceding term is the difference of an arithmetic progression. It is always same for the same arithmetic progression.

5 0
2 years ago
Other questions:
  • Riders travel at a average speed of 61 feet per second for 3118 feet. A maximum of 187 per second. What is this as an expression
    9·1 answer
  • What is 8(m-3)=56 mean
    12·1 answer
  • Solve the system of linear equations below.
    10·1 answer
  • Can someone please help me??
    14·1 answer
  • What is the product (4x)( -3x^6)(-7x^3)
    7·1 answer
  • 2. Mary is an authorized user on her parents' credit card. What may happen if Mary doesn't use the card in a responsible way? Ma
    15·1 answer
  • 1) Calcule:
    8·1 answer
  • A marketing consultant observed 40 consecutive shoppers to estimate the average money spent by shoppers in a supermarket store.
    10·1 answer
  • Math gram question please help thanks
    5·1 answer
  • Please help me with this for brainliest
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!