Respuesta :
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:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
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:
[tex]A(t) = 1000(1.0215)^{4t}[/tex]
Comparing to the general formula.
[tex]P = 1000[/tex]
[tex]1 + \frac{r}{n} = 1.0215[/tex]
[tex]nt = 4t[/tex]
From the last one:
[tex]n = 4[/tex]
Which means 4 compoundings per year. This means that the interest is compounded quarterly.
Interest rate:
[tex]1 + \frac{r}{n} = 1.0215[/tex]
Since n = 4.
[tex]\frac{r}{4} = 1.0215 - 1[/tex]
[tex]\frac{r}{4} = 0.0215[/tex]
[tex]r = 4*0.0215[/tex]
[tex]r = 0.0860[/tex]
So the interest rate is of 8.60%.
Answer:
the answer is quarterly and 8.88
Step-by-step explanation:
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