Question

Emma put $98,000 in an account earning interest compounded annually. At

Answer 1

Answer:

The interest rate was of 5.5% a year.

Step-by-step explanation:

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.

In this question, we have that:

$A = 109076.45, P = 98000, n = 1, t = 2$

We have to find r.

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

$109076.45 = 98000(1 + r)^{2}$

$(1+r)^{2} = \frac{109076.45}{98000}$

$(1+r)^{2} = 1.113025$

Taking the square root from both sides to isolate r.

$\sqrt{(1+r)^{2}} = \sqrt{1.113025}$

$1 + r = 1.055$

$r = 1.055 - 1$

$r = 0.055$

The interest rate was of 5.5% a year.