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:
[tex]A = P (1 + r)^t[/tex]
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:
First, let's calculate the P in the equation.
You put $7,500 each year for 3 years, so multiply 7,500 by 3.
[tex](7,500) * (3) = 22,500[/tex]
Next, let's start putting everything into the equation, like this:
[tex]A = 22,500(1 + .05)^3[/tex]
(When doing interest rate you have to move the decimal over twice)
Now that we have the equation, let's solve it!
[tex]A = 22,500(1.05)^3\\A = 22,500(1.15763)\\A = 26,046.6[/tex]
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
[tex]A = 36046.6(1.05)^1\\A = 37848.9[/tex]
Thus, the final answer will be $37,848.9
Hope this helps!
- Kay :)
After saving the money for the four years and by adding $10,000 in the end of fourth year the money the amount that will be saved is $48,942.23.
The temporal value of money is based on the simple notion that one dollar today is worth more than one dollar in the future. This is because one can invest the dollar they have today and have it increase at a rate of return, or interest, over time.
The formula for future value is-
[tex]\begin{aligned}\text{FV}&=\text{CF}\times\dfrac{(1+r)^n-1}{\text{r}}+\text{FV}\\&=\$7,500\times\dfrac{(1+0.05)^4-1}{0.05}+\$7,500\\&=\$48,942.23\end{aligned}[/tex]
Thus, the future value by the end of the fourth year is $48,942.23.
For further details about the future value refer to this link:
https://brainly.in/question/40202543
