Question

If $3800 is invested in a savings account for which interest is compounded
quarterly, and if the $3800 turns into $4300 in 2 years, what is the interest
rate of the savings account?

Answer 1

Answer:

Step-by-step explanation:

The formula to use for this is

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

For us,

A(t) = 4300

P = 3800

n = 4

t = 2

r = ?

Let's fill in what we have then:

$4300=3800(1+\frac{r}{4})^{(4)(2)}$

which simplifies a tiny bit to

$4300=3800(1+\frac{r}{4})^8$

The first thing to do is to divide both sides by 3800 to get

$\frac{4300}{3800}=(1+\frac{r}{4})^8$

Now take the 8th root of both sides (on your calculator, of course!) to get

$1.01557174=1+\frac{r}{4}$

Now subtract 1 from both sides to get

$.01557174=\frac{r}{4}$

And multiply both sides by 4 to get

.0622869598 = r

Multiply by 100 to get the rate as a percentage.  It rounds to

r = 6.23%

Answer 2

Answer:

6.22%

Step-by-step explanation: