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 \(A=P(1+\frac{r}{n})^{nt}\)
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
\(6600=5700(1+\frac{r}{4})^{(4)(4)}\)
\(\frac{66}{57}=(1+\frac{r}{4})^{16}\)
By taking log on both the sides of the equation
\(log(\frac{66}{57})=log(1+\frac{r}{4})^{16}\)
\(log66-log57=16log(1+\frac{r}{4)}\)
1.8195-1.7558=16log(1+\(\frac{r}{4})\)
0.0637 = \(16log(1+\frac{r}{4})\)
\(\frac{0.0637}{16}=log(1+\frac{r}{4})\)
.00398=\(log(1+\frac{r}{4})\)
\(1+\frac{r}{4}=10^{.00398}=1.0092\)
\(\frac{r}{4}=1.0092-1=.0092\)
r = 4×0.0092 = 0.0368
Or r = 0.0368×100 = 3.68%
