Question

You are saving money for a down payment on a new house. You intend to place $7,500 at the end of each year for three years into an account earning 5% per year. At the end of the fourth year, you will place $10,000 into this account. How much money will be in the account at the end of the fourth year?

Answer 1

Answer:

$37,848.9

Explanation:

We can use the interest rate formula to figure out how much is in the account after the first 3 years. The interest rate formula is show below:

$A = P (1 + r)^t$

Let me delineate what each part of this equation means:

A = The total amount

P = The initial amount of money put into the account

R = the interest rate

T = Time

The equation gives us the following:

• You place $7,500 each year for three years
• The interest rate is 5%
• At the end of the 4th year $10,000 will be placed in the account

First, let's calculate the P in the equation.

You put $7,500 each year for 3 years, so multiply 7,500 by 3.

$(7,500) * (3) = 22,500$

Next, let's start putting everything into the equation, like this:

$A = 22,500(1 + .05)^3$

(When doing interest rate you have to move the decimal over twice)

Now that we have the equation, let's solve it!

$A = 22,500(1.05)^3\\A = 22,500(1.15763)\\A = 26,046.6$

After 3 years $26,046.6 is in the account.

But, don't forget the last part of the question!

But you have a fourth year too!

Add the $10,000 onto the $26,046.6

That equals $36,046.6.

Lets plug this back into the equation for the final year

$A = 36046.6(1.05)^1\\A = 37848.9$

Thus, the final answer will be $37,848.9

Hope this helps!

- Kay :)

Answer 2

Answer:

you earn  7,510

Explanation: