Answer:
It would be $1,590.75 more if it were compounded quarterly than monthly.
Step-by-step explanation:
In order to solve this problem, you need to understand the Compound Interest Formula.
[tex]A= P(1 + \frac{r}{n})^t[/tex]
Where A is the Amount, P is the principal or the initial amount received, r is the rate, n is the number of times (per year) it is compounded, and t is the time in years.
The question gives you all of the information to input into the formula. You have the principal, $5000, the rate, 6% (.06), it's being compounded monthly (12 & 4 per year), and we have the years, 25.
We need to compare the two formulas where the only thing that will change is n. n will be 12 (compounded monthly) and 4 (compounded quarterly).
Compounded monthly
[tex]A=5000(1+\frac{0.06}{12})^{25}\\A = 5663.98[/tex]
Compounded monthly, the account would have $5,663.98 or $5,664 (simplified).
Compounded quarterly
[tex]A=5000(1+\frac{0.06}{4})^{25}\\A =7254.73[/tex]
Compounded quarterly, the account would have $7,254.73 or $7,255 (simplified).
Now, we need to find the difference between monthly and quarterly.
7254.73 - 5663.98 = $1,590.75
It would be $1,590.75 more if it were compounded quarterly than monthly.
