Answer
a) $\$ 7401.22$
b) $\$ 7459.12$
Work Step by Step
We are given an initial invest of $P_0=5000$, and an interest rate of $4 \%$ per year.
a) If interest is compounded annually, we have $P=5000(1.04)^t$. After $t= 10$ years, the amount in the account is $5000(1.04)^{10}= \$ 7401.22$.
b) If interest is compounded continuously, we have $P=5000 e^{0.04 t}$. After $t= 10$ years, the amount in the account is $5000 e^{0.04(10)}=\$ 7459.12$.
This is expected, the account contains more money if the interest is compounded continuously.
