Zoey opened a savings account four years ago with a deposit of $935.15. The interest on the account compounds monthly. If Zoey’s current account balance is $1,128.16, what is the interest rate on the account?

0.4%

4.7%

14.2%

18.9%

Question

Zoey opened a savings account four years ago with a deposit of $935.15. The interest on the account compounds monthly. If Zoey’s current account balance is $1,128.16, what is the interest rate on the account? 

 0.4% 

 4.7% 

 14.2% 

 18.9%

anonymous · Answer

@jdoe0001  can u help on this one?

anonymous · Answer

Don't want the answer I wanna know how to find it? :)

jdoe0001 · Answer

sorry the system is a bit lagged....

you know the compound interest equation, right?

jdoe0001 · Answer

anyhow, the compound interest balance, can be found by 
$\bf b = balance\
p = principal\
r = rate\
n = periods\
t = years\ \quad \ \quad \
b = p\left(1+\cfrac{r}{n}\right)^{nt}$

jdoe0001 · Answer

so you need the rate, that is, you need "r"
so let's solve for "r"

jdoe0001 · Answer

$\bf b = balance\
p = principal\
r = rate\
n = periods\
t = years\ \quad \ \quad \
b = p\left(1+\cfrac{r}{n}\right)^{nt}\\ \quad \
\cfrac{b}{p} = \left(1+\cfrac{r}{n}\right)^{nt}\
\textit{taking "nt" root from both sides}\
\large {\sqrt[nt]{\cfrac{b}{p}} = 1+\cfrac{r}{n} \implies \sqrt[nt]{\cfrac{b}{p}}-1 = \cfrac{r}{n}\ \quad \implies 
n\cdot \left(\sqrt[nt]{\cfrac{b}{p}}-1\right) = r}$