Question

The expression 1,000(1.0215)4t represents the amount of money in an account after t years.

Answer 1

Answer:

The interest is compounded quarterly.

The effective annual interest rate on the account is 8.60%.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

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

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.

We are given:

$A(t) = 1000(1.0215)^{4t}$

Comparing to the general formula.

$P = 1000$

$1 + \frac{r}{n} = 1.0215$

$nt = 4t$

From the last one:

$n = 4$

Which means 4 compoundings per year. This means that the interest is compounded quarterly.

Interest rate:

$1 + \frac{r}{n} = 1.0215$

Since n = 4.

$\frac{r}{4} = 1.0215 - 1$

$\frac{r}{4} = 0.0215$

$r = 4*0.0215$

$r = 0.0860$

So the interest rate is of 8.60%.