Respuesta :
The amount of interest earned would be $134.87 for a total of $634.87 after 6 years.
Explanation:
The formula for compound interest is
[tex]A=p(1+\frac{r}{n})^{tn}[/tex],
where p is the principal, r is the interest rate as a decimal number, n is the number of times per year the interest is compounded, and t is the number of years.
Our principal is $500, our interest rate is 4%=4/100=0.04, n is 4, and t is 6:
[tex]A=500(1+\frac{0.04}{4})^{4\times6} = 500(1+0.01)^{24}=500(1.01)^{24}[/tex]
Evaluating this, we get $634.87, which means there was 634.87-500 = 134.87 earned in interest.
Explanation:
The formula for compound interest is
[tex]A=p(1+\frac{r}{n})^{tn}[/tex],
where p is the principal, r is the interest rate as a decimal number, n is the number of times per year the interest is compounded, and t is the number of years.
Our principal is $500, our interest rate is 4%=4/100=0.04, n is 4, and t is 6:
[tex]A=500(1+\frac{0.04}{4})^{4\times6} = 500(1+0.01)^{24}=500(1.01)^{24}[/tex]
Evaluating this, we get $634.87, which means there was 634.87-500 = 134.87 earned in interest.
Answer:
$634.87.
Step-by-step explanation:
We are supposed to find the total amount of an amount of $500 principal earning 4% compounded quarterly after 6 years.
To solve our given problem we will use compound interest formula to solve our given problem.
[tex]A=P(1+\frac{r}{n})^{nt}[/tex], where,
A = Final amount after t years,
P = Principal amount,
r = Interest rate in decimal form,
n = Number of times interest is compounded per year,
t = Time in years.
First of all, we need to convert our given interest rate in decimal form.
[tex]4\%=\frac{4}{100}=0.04[/tex]
Upon substituting our given values in above formula we will get,
[tex]A=500(1+\frac{0.04}{4})^{4*6}[/tex]
[tex]A=500(1+0.01)^{24}[/tex]
[tex]A=500(1.01)^{24}[/tex]
[tex]A=500*1.2697346485[/tex]
[tex]A=634.867\approx 634.87[/tex]
Therefore, there will be an amount of $634.87 in the account after 6 years.
