$5326.135 will be his ending balance after one year.
Solution:
Deposited amount = $2,300
Rate of interest = 1.13% per week
[tex]A=P\left(1+\frac{r}{n}\right)^{n t}[/tex]
where A = final amount
P = principal = 2300
r = interest rate = [tex]1.13\%=\frac{1.13}{100}=0.0113[/tex]
n = number of times interest applied per time period = 52 week
(1 year has 52 weeks)
t = number of time periods elapsed = 1 year
On substituting the values we get,
[tex]Amount=2300 \times\left(1+\frac{0.0113}{52}\right)^{52}[/tex]
[tex]\Rightarrow2300\times(\frac{52+0.0113}{52})^{52}\rightarrow2300\times(\frac{52.0113}{52})^{52}\rightarrow2300\times(1.000217)^{52}[/tex]
On solving we get, [tex]\Rightarrow5326.135[/tex]
Therefore, the amount is $5326.135.
