Total amount in the saving account after 5 years in which the annual interest, compounded continuously, is $15,103.85.
Compound interest is the amount charged on the principal amount and the accumulated interest with a fixed rate of interest for a time period.
The formula for the final amount with the compound interest formula can be given as,
[tex]A=P\times\left(1+\dfrac{r}{100n}\right)^{nt}\\[/tex]
Here, A is the final amount (principal plus interest amount) on the principal amount P of with the rate r of in the time period of t.
$13,000 is deposited into a savings account with an annual interest rate of 3% compounded continuously.
The amount in account after 5 years can be calculated with the above formula as,
[tex]A=13000\times\left(1+\dfrac{3}{12\times100}\right)^{12\times5}\\A=15101.02[/tex]
The total amount in the saving account after 5 years in which the annual interest, compounded continuously, is $15,103..85.
Learn more about the compound interest here;
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