A non-integer answer should be entered as a decimal, rounded to the hundredths place.

Suppose you'd like to save enough money to pay cash for your next car. The goal is to save an extra $28,000 over the next 6 year

Anna35 [415]

Given:

• Amount to save, A = $28,000

,

• Time, t = 6 years

,

• Interest rate, r = 5.3% ==> 0.053

,

• Number of times compounded = quarterly = 4 times

Let's find the amount that must be deposited into the account quarterly.

Apply the formula:

$FV=P(\frac{(1+\frac{r}{n})^{nt}-1}{\frac{r}{n}})$

Where:

FV is the future value = $28,000

r = 0.053

n = 4

t = 6 years

Thus, we have:

$28000=P(\frac{(1+\frac{0.053}{4})^{4\times6}-1)}{\frac{0.053}{4}}$

Let's solve for P.

We have:

$\begin{gathered} 28000=P(\frac{(1+0.01325)^{24}-1}{0.01325}) \\ \\ 28000=P(\frac{(1.01325)^{24}-1)^{}}{0.01325}) \\ \\ 28000=P(\frac{1.371509114-1}{0.01325}) \\ \\ 28000=P(\frac{0.371509114}{0.01325}) \end{gathered}$

Solving further:

$28000=P(28.0384237)$

Divide both sides by 28.0384237:

$\begin{gathered} \frac{28000}{28.0384237}=\frac{P(28.0384237)}{28.0384237} \\ \\ 998.6=P \\ \\ P=998.6 \end{gathered}$

Therefore, the amount that must be deposited quarterly into the account is $998.60

ANSWER:

$998.60

8 0

1 year ago

Raphael deposited $6,500 in an account that pays 4.25% interest, compounded annually. He left the money in the account for 4 yea

netineya [11]

Answer:

$1105

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 4.25%/100 = 0.0425 per year,

then, solving our equation

I = 6500 × 0.0425 × 4 = 1105

I = $ 1,105.00

The simple interest accumulated

on a principal of $ 6,500.00

at a rate of 4.25% per year

for 4 years is $ 1,105.00.

6 0

3 years ago

6. Use synthetic division to completely factor y = x3 + 2x2 – 5x - 6 by x + 1.

navik [9.2K]

Answer:

y = (x + 1)(x + 3)(x - 2)

Step-by-step explanation:

attached

3 0

3 years ago

Parker is laying pavers to build a patio in his backyard. Each square paver measures 2 feet on each side. He would like the pati

MatroZZZ [7]

Answer:

32 pavers

Step-by-step explanation:

step 1

Find out the area of one square paver

The area of a square is

$A=s^{2}$

where

s is the length side of the square

we have

$s=2\ ft$

substitute

$A=2^{2}\\A=4\ ft^{2}$

step 2

Find out the area of the rectangular patio

we know that

The area of a rectangle is

$A=LW$

we have

$L=16\ ft\\W=8\ ft$

substitute

$A=(16)(8)\\A=128\ ft^2$

step 3

Find out the number of pavers needed to build the patio

Divide the area of the rectangular patio by the area of one paver

$128\ ft^2/4\ ft^{2}=32\ pavers$

5 0

3 years ago

Express the ratio in simplest form. The ratio of 500 m to 3 km

tester [92]

1) Express the following ratios in the simplest form.
a) 150 : 400
Solution : 
The given ratio is 150 : 400 = 150/400
The common factor of 150 and 400 is 50.
(150 ÷ 50)/ (400 ÷ 50) = 3/8 = 3 : 8.
----------------------------------------------------------------------
b) A dozen to score
Solution : 
One dozen = 12 and one score = 20.
So, a dozen to score = 12/20 = 12 : 20.
(12 ÷ 4)/ (20 ÷ 4) [ As the common factor is 4]
= 3/5 = 3 : 5.
----------------------------------------------------------------------
c) 200 grams to 4 kg
Solution : 
200 g to 4 kg
As both the quantities are in different units, first make their units same.
1kg = 1000 g
∴ 4 kg = 4000 g.
200 g to 4000 g = 200 / 4000
Common factor of 200 and 4000 is 200.
(200 ÷ 200)/(4000 ÷ 200) = 1/20 = 1 : 20.
----------------------------------------------------------------------
d) Sam earned $4000 and paid $500 as income tax and spent $1500 on household expenses. Find the ratio of : 1) income tax to income 2) household expenses to income 3) savings to earnings
Solution 
Sam’s income = $4000
Income tax = $500
∴ income tax to income = 500/4000
(500 ÷ 500)/(4000 ÷ 500) = 1/8
Ratio of Income tax to income is 1 : 8
Expenses = $1500
∴ Household expenses to income = 1500/4000
(1500 ÷ 500)/ (4000 ÷ 500) = 3/8
Ratio of Household expenses to income = 3 : 8.
Savings = Income – (expenses + income tax)
Savings = 4000 – (1500 + 500) = $2000.
∴ Savings to earnings = 2000/4000
(2000 ÷ 2000)/(4000 ÷ 2000) = ½
Ratio of savings to expenses = 1 : 2.

3 0

4 years ago