Answer
The second investment is worth more after 5 years.
The first investment is worth more after 10 years.
Work Step by Step
After 5 years, the first investment is worth:
$$
P=1000\left(1+\frac{0.05}{12}\right)^{12(5)}=\$ 1283.36
$$
After 5 years, the first investment is worth:
$$
P=1100 e^{0.04(5)}=\$ 1343.54
$$
Hence, the second investment is worth more after 5 years.
After 10 years, the first investment is worth:
$$
P=1000\left(1+\frac{0.05}{12}\right)^{12(10)}=\$ 1647.01
$$
After 10 years, the first investment is worth:
$$
P= 1100 e^{0.04(10)}=\$ 1641.01
$$
Hence, the first investment is worth more after 10 years.
