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mote1985 [20]
3 years ago
8

Samuel currently has an account balance of $3,439.96. He opened the account five years ago with a deposit of $3,104.31. If the i

nterest compounds quarterly, what is the interest rate on the account?
Mathematics
1 answer:
iogann1982 [59]3 years ago
5 0

Answer:

The interest rate on the account is 2.1%

Step-by-step explanation:

Compound interest is one that is added to the initial capital and on which new interests are generated. Money, in this case, has a multiplier effect because interest produces new interest. In other words, the initial capital increases in each period because the interests add up.

To calculate the final capital, the initial capital is multiplied by one plus the interest, raised to the number of periods:  

A=P*(1+\frac{r}{n}) ^{n*t}

where

  • A = Accumulated amount (principal + interest)
  • P = Principal amount
  • r = the interest rate
  • n = the number of times the interest is compounded per year
  • t = Time Involved in years

In this case:

  • A = $3,439.96
  • P = $3,104.31
  • r = ?
  • n = 4
  • t = 5

Replacing, you get:

3,439.96=3,104.31*(1+\frac{r}{4}) ^{4*5}

Now, solving:

\frac{3,439.96}{3,104.31} =(1+\frac{r}{4}) ^{20}

\sqrt[20]{1.1081}  =(1+\frac{r}{4})

1.00514 =1+\frac{r}{4}

1.00514 -1=\frac{r}{4}

0.00514=\frac{r}{4}

r=0.0051*4

r= 0.02056

In percentage it is expressed as: r= 2.056 %≅ 2.1 %

<u><em>The interest rate on the account is 2.1%</em></u>

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A passenger train has tickets available for 12 window seats and 8 aisle seats. The next person to buy a ticket will be randomly
Svetradugi [14.3K]

Answer:

2/5

Step-by-step explanation:

There is an 8/20 chance that the next person will receive a window seat. You simplify that probability to get your answer. 8/20 becomes 2/5. So the answer is 2/5.

7 0
2 years ago
what is the rate of inflation if a savings account has a nominal interest rate of 3% and a real interest rate of 1%
IgorLugansk [536]

Answer:

the rate of inflation is 2%.

Step-by-step explanation:

given:

Nominal interest rate =3%

Real interest rate=1%

To Find:

Rate of inflation=?

Solution:

Nominal interest rate:

Nominal interest rate refers to the interest rate before taking inflation into account.

Inflation rate:

The inflation rate is the percent increase or decrease in prices during a specified period. It's usually over a month or a year.

Real interest rate:

A real interest rate is an interest rate that has been adjusted to remove the effects of inflation to reflect the real cost of funds to the borrower and the real yield to the lender or to an investor.

Real interest rate ≈ nominal interest rate − inflation rate.

This can be re written as

inflation rate= Real interest rate - nominal interest rate

Substituting the values,

inflation interest = 1+3

inflation interest=4%

i hope this helpsss<3

:)

if u didnt undersstand make sure to tell me so i can try to say it again

7 0
3 years ago
Let A {a, b, c, d}. Find the power set of A, PA
Nina [5.8K]

A=\{a,b,c,d\}\\|A|=4\\\mathcal{P}(A)=2^4=16

8 0
3 years ago
Midpoint of (1,3) and (4,-5)
crimeas [40]

Answer:

The rigth answer is, ( 5/2 , -1 )

Step-by-step explanation:

To find the midpoint we use the respective formula:

m = ( x1 + x2 / 2 ,  y1 + y2 / 2 )

We replace:

m = ( 1 + 4/2  ,  3 + (- 5) / 2 )

We solve:

m = ( 5/2 ,  -1 )

5 0
3 years ago
3(x + 1) = -2 (x - 1) -4
AlekseyPX

Answer:

x = -1

Step-by-step explanation:

use distribution

3x + 3 = -2x + 2 - 4

simplify

3x + 3 = -2x - 2

combine like terms

3x + 3 = -2x - 2

-3x                -3x

3 = -5x - 2

+2         +2

5 = -5x

/-5     /-5

-1 = x

7 0
3 years ago
Read 2 more answers
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