Answer:
Rate of interest = 3.68%
Step-by-step explanation:
If $5700 is invested in a savings account for which interest is compounded quarterly.
$5700 turns into $6600 in 4 years
Compound interest formula will be [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Here A = Future amount
P = principal amount
r = rate of interest
n = number of times money is compounded
t = time
Now we put the values given in the question
[tex]6600=5700(1+\frac{r}{4})^{(4)(4)}[/tex]
[tex]\frac{66}{57}=(1+\frac{r}{4})^{16}[/tex]
By taking log on both the sides of the equation
[tex]log(\frac{66}{57})=log(1+\frac{r}{4})^{16}[/tex]
[tex]log66-log57=16log(1+\frac{r}{4)}[/tex]
1.8195-1.7558=16log(1+[tex]\frac{r}{4})[/tex]
0.0637 = [tex]16log(1+\frac{r}{4})[/tex]
[tex]\frac{0.0637}{16}=log(1+\frac{r}{4})[/tex]
.00398=[tex]log(1+\frac{r}{4})[/tex]
[tex]1+\frac{r}{4}=10^{.00398}=1.0092[/tex]
[tex]\frac{r}{4}=1.0092-1=.0092[/tex]
r = 4×0.0092 = 0.0368
Or r = 0.0368×100 = 3.68%
