Answer:
A. 2.2% is correct.
Step-by-step explanation:
Deposit Amount = $60
Pearl saving $60 into an account with interest is compounded monthly.
Her money is double in approximately 33 years.
Formula
[tex]A=P\left ( 1+\frac{r}{n} \right )^{n\times t}[/tex]
where,
A is final amount. (Double of initial value). A=$120
P is deposit amount. P=$60
r is rate of interest. r=?
n number of period. n=12
t is total time. t=33
Substitute all these values into formula.
[tex]120=60\left ( 1+\frac{r}{1200} \right )^{12\times 33}[/tex]
Now we solve for r
[tex]\left ( 1+\frac{r}{1200} \right )^{396}=2[/tex]
Taking log both sides
[tex]396\log\left ( 1+\frac{r}{1200} \right )=\log 2[/tex]
[tex] \log\left ( 1+\frac{r}{1200} \right )=0.00076[/tex]
[tex]1+\frac{r}{1200}=10^{0.00076}[/tex]
[tex]r=1200(1.00179-1)[/tex]
[tex]r=2.2\%[/tex]
Thus, Rate of interest is 2.2%
