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A bank offers all savings accounts 5% interest compounded annually. If one account has a principal of $100 and another

arsen [322]

Answer:

From the calculation for both the accounts, it is clear that both the account double in the same time period of 14 years 26 days .

Step-by-step explanation:

Given as :

The principal for the first account = p = $100

The rate of interest = r = 5% compounded annually

The account gets double , so, Amount = A = $200

Let the time after which account gets double = t years

So<u>, From Compound Interest method</u>

Amount = Principal × $(1+\dfrac{\trxtrm rate}{100})^{\textrm time}$

As amount is double its principal

So, A = 2 × $100 = $200

Or, A = p × $(1+\dfrac{\trxtrm r}{100})^{\textrm t}$

Or, $200 = $100 × $(1+\dfrac{\trxtrm 5}{100})^{\textrm t}$

Or, $\dfrac{200}{100}$ = $(1.05)^{\textrm t}$

Or, 2 = $(1.05)^{\textrm t}$

Taking Log both side

$Log_{10}2$ = $Log_{10}(1.05)^{t}$

Or, 0.3010 = t $Log_{10}1.05$

Or, 0.3010 = t × 0.0211

∴ t = $\dfrac{0.3010}{0.0211}$

I.e t = 14.26

So, The time period to get account double is 14 years 26 days

<u>Again </u>

Amount = Principal × $(1+\dfrac{\trxtrm rate}{100})^{\textrm time}$

Or, A = p × $(1+\dfrac{\trxtrm r}{100})^{\textrm t}$

As amount is double its principal

So, A = 2 × $1000 = $2000

Or, $2000 = $1000 × $(1+\dfrac{\trxtrm 5}{100})^{\textrm t}$

Or, $\dfrac{2000}{1000}$ = $(1.05)^{\textrm t}$

Or, 2 = $(1.05)^{\textrm t}$

Taking Log both side

$Log_{10}2$ = $Log_{10}(1.05)^{t}$

Or, 0.3010 = t $Log_{10}1.05$

Or, 0.3010 = t × 0.0211

∴ t = $\dfrac{0.3010}{0.0211}$

I.e t = 14.26

So, The time period to get account double is 14 years 26 days

Hence From the calculation for both the accounts, it is clear that both the account double in the same time period of 14 years 26 days . Answer

7 0

3 years ago

Which process will transform Figure A onto Figure B ?

Karolina [17]

Answer:

1st option

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Given the system of equations presented here: 3x + 5y = 29 x + 4y = 16 Which of the following actions creates an equivalent syst

Snezhnost [94]

Multiply the 2nd equation by -3 to get -3x-12y = -48.

6 0

3 years ago

Read 2 more answers

Michaela walked 2/5 mile to the store in 1/4 hour. What is her walking pace?

rusak2 [61]

Her walking pace is:
$\frac{8}{5}$

Solution

$\frac{2}{5} \div \frac{1}{4 } \\ \frac{2}{5} \times \frac{4}{1} = \frac{8}{5}$

8 0

4 years ago

Read 2 more answers

Last year there were 1,435 8thgrade students enrolled at your school. This year there are 1,220. What is the percent change in t

julsineya [31]

Hi there!

Answer:

-14.98%(or -15%).

Step-by-step explanation:

1)To find the percent decrease,all you have to do is minus the original number from the decreased amount so:

1435-1220= 215

2)Then you divide this answer by the original number again so:

215÷1435= 0.1498

3)Then you times the decimal by 100 so:

0.1489x100= -14.98%(or -15%).

Hope this helps!

7 0

4 years ago