Question

$500 principal earning 4% compounded quarterly after 6 years

Answer 1

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
$A=p(1+\frac{r}{n})^{tn}$,

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:
$A=500(1+\frac{0.04}{4})^{4\times6} = 500(1+0.01)^{24}=500(1.01)^{24}$

Evaluating this, we get $634.87, which means there was 634.87-500 = 134.87 earned in interest.

Answer 2

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.

$A=P(1+\frac{r}{n})^{nt}$, 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.

$4\%=\frac{4}{100}=0.04$

Upon substituting our given values in above formula we will get,

$A=500(1+\frac{0.04}{4})^{4*6}$

$A=500(1+0.01)^{24}$

$A=500(1.01)^{24}$

$A=500*1.2697346485$

$A=634.867\approx 634.87$

Therefore, there will be an amount of $634.87 in the account after 6 years.