Question

If $5700 is invested in a savings account for which interest is compounded quarterly, and if the $5700 turns into $6600 in 4 years, what is the interest rate of the savings account?

Answer 1

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%

Answer 2

The interest rate is 3.68%, can I get brainliest answer? Thanks :)