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alexdok [17]
4 years ago
5

The amount of money in a bank account that is compounded yearly can be represented by the function A(y) = P(1 + r)y, where P is

the amount initially deposited, r is the annual interest rate expressed as a decimal, and y is the number of years that have passed since the initial deposit. $2,700 was deposited 14 years ago into a bank account that is compounded yearly, and no additional deposits or withdrawals have been made. If the amount of money now in the bank account is $7,930.42, what is the annual interest rate?
A) about 5%
B) about 6%
C) about 7%
D) about 8%
Mathematics
2 answers:
pochemuha4 years ago
6 0

Answer:

The correct option is D. The interest is about 8%.

Step-by-step explanation:

The amount of money in a bank account that is compounded yearly can be represented by the function

A(y)=P(1+r)^y

Where P is the amount initially deposited, r is the annual interest rate expressed as a decimal, and y is the number of years that have passed since the initial deposit.

The initial amount is $2700, numbers of years is 14 and the amount after 14 years is $7930.42.

7930.42=2700(1+r)^{14}

2.937=(1+r)^{14}

Taking log both sides.

log2.937=log(1+r)^{14}        (loga^b=bloga)

0.4679=14log(1+r)

0.033422=log(1+r)

10^{0.033422}=10^{log(1+r)}

1.079999=1+r            (10^{loga}=a)                        

0.079999=r

r\approx 0.08

Therefore the correct option is D. The interest is about 8%.

8_murik_8 [283]4 years ago
3 0

Answer:

D

Step-by-step explanation:

7930.42 = 2700(1+r)¹²

(1+r)¹⁴ = 2.9371925926

14×ln(1+r) = ln2.9371925926

ln(1+r) = 0.076961016

1+r = e^0.076961016

1+r = 1.0799999729

r = 0.0799999729 × 100

= 8%

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masha68 [24]
The one ur selecting is the correct one!
5 0
3 years ago
2. Lorena is trying to choose between two different savings accounts at H-Town Bank. She will deposit $3,500 dollars and will le
Ivahew [28]

Answer:

First of all, this question is not complete. So, we will be hypothetically create two accounts and try to choose the one with the greater profit.

Choice 1 = X = Final Amount after 12 years = $5600

Choice 2 = Y = Final Amount after 12 years = $6285.50

Hence, Lorena should choose choice 2, as it gives more profit over than choice 1.

Step-by-step explanation:

First of all, this question is not complete. So, we will be hypothetically create two accounts and try to choose the one with the greater profit.

Initial Deposit Amount = $3500

Time period = 12 years

Let's Suppose Lorena has two X and Y choices of accounts at H-town Bank.

X = simple interest of 5% over the initial amount for 12 years.

Y = Compound interest 5% over the initial amount for 12 years.

Solution:

Let's calculate the profit for choice 1 = X

Simple interest = 5%

Initial amount = $3500

Time period = 12 years

Formula = A = P (1 + rt)

where, A = Final amount after 12 years

t = time period in years  = 12

P = initial amount to be deposited = $3500

r = annual interest rate = 5%

Plug in the values to get the total amount.

A = 3500(1+0.05x12)

A = $5600 = final amount Lorena will get after 12 years.

Let's calculate the profit for choice 2 = Y

Compound interest = 5%

Initial amount = $3500

Time period = 12 years

Formula = A = P (\frac{r}{n} + 1)^{nt}

where,

A = Final amount after 12 years

t = time period in years  = 12

P = initial amount to be deposited = $3500

r = annual interest rate = 5%

n = number of times interest rate is applied or compounded. = 12

Plug in the values to get the total amount.

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

A = $6285.50

Hence, Lorena should choose choice 2, as it gives more profit over than choice 1.

4 0
3 years ago
please i have been stuck on thos math problem for 123 minutes ago please help please I'm stressing out please I urgently need he
alisha [4.7K]

Answer:

it could be    1. c      2. a      3. d      4. b

or it could be the answers i did for last time in the pic: (that is my old account that got banned)

but i think the answers that are right are the ones i did rn of  1. c      2. a      3. d      4. b

8 0
4 years ago
A number divided by three less two is at most two
zheka24 [161]

Answer:

6

Step-by-step explanation:

6/3 = 2

5 0
3 years ago
Find the inverse of f(x)=(x−5)/(−4x−2)
uysha [10]

Answer:

{f}^{ - 1} (x)= \frac{  5 - 2x }{ 4x  + 1}

Step-by-step explanation:

The given rational function is

f(x) =  \frac{x - 5}{ - 4x - 2}

Let

y =  \frac{x - 5}{ - 4x - 2}

Interchange x and y

x=  \frac{y- 5}{ - 4y - 2}

Cross multiply

x( - 4y - 2)= y- 5

Expand

- 4xy   - 2x= y- 5  \\ - 4xy  - y=  2x - 5 \\y( - 4x - 1)=  2x - 5

Solve for y;

y= \frac{  2x - 5}{ - 4x - 1}

or

y= \frac{  5 - 2x }{ 4x  + 1}

Therefore

{f}^{ - 1} (x)= \frac{  5 - 2x }{ 4x  + 1}

7 0
3 years ago
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