Question

Eliot opens a savings account with $5,000. He deposits $50 every month into the account that compounds annually and has a 0.95% interest rate. What will his account total be in 5 years?

Answer 1

Answer:

$8,328.65

Step-by-step explanation:

First we need take the number of deposits and add the amount to the initial amount in the account.

$50 x 12Months = $600

Initial Amount = $5,000

Now we convert the interest rate into decimal to make things easier.

0.95% = 0.0095

Now that we have the principal amount, we can then use the formula $A = P (1 + r)^{t}$.

We need to keep in mind that the value for time will have to stay in a constant value as the total deposits each year will affect the amount.

Now let's begin with the amount for the first year:

$A = P (1 + r)^{t}$.

$A = 5,600 (1 + 0.0095)^{1}$

A = 5,600 ( 1.0095 )

A = 5,653.20 Year 1

Now let's proceed to the next year. Remember that the deposits that Eliot make total at $600 each year.

P = 5,653.20 + 600

P = 6,253.20

Now we can proceed to calculate for the amount of the second year:

[tex]A = 6253.2 (1.0095)^{1}[/text]

A = 6,253.2 ( 1.0095 )

A = 6,312.61 Year 2

Now let's proceed doing the same process until the 5th year.

Year 3 Computation:

P = 6,312.61 + 600

P = 6,912.61

[tex]A = 6912.61 (1.0095)^{1}[/text]

A = 6978.28 Year 3

Year 4 Computation:

P = 6,978.28 + 600

P = 7,578.28

[tex]A = 7,578.28 (1.0095)^{1}[/text]

A = 7,650.27 Year 4

Last but no the least year 5.

P = 7,650.27 + 600

P = 8,250.27

[tex]A = 8,250.27 (1.0095)^{1}[/text]

A = 8,328.65 Year 5

So now we can conclude that at the end of year 5, Eliot will have a total of:

$8,328.65 in his account.