Number problem

Hello, Paulo1913!

Quote:

Jemima has $5000 to invest for two and a half years.
Her bank offers two different investment schemes:
. . an account that pays 3.25% interest at the end of each year,
. . an account that pays 1.3% interest at the end of each six months.

Investigate each scheme and recommend to Jemima, with reasons, what she should do.

You're expected to know the compound interest formula:

$\displaystyle A \;=\;P\left(1 + \frac{i}{n}\right)^n$

. . where: .$\displaystyle \begin{Bmatrix}P & = & \text{principal invested} \\ i & = & \text{periodic interest rate} \\ n & = & \text{number of periods} \\ A & = & \text{final balance} \end{Bmatrix}$

Plan A has: .$\displaystyle \begin{array}{ccc}P & = & 5000 \\ i & = & 0.0325 \\ n & = & 2.5 \end{array}$

$\displaystyle A \;=\;5000(1.0325)^{2.5} \;\approx\;\boxed{\$5,416.21}$

Plan B has: .$\displaystyle \begin{array}{ccccc}P & = & 5000 \\ i & = & 0.013/2 & = 0.0065 \\ n & = & 5\end{array}$

$\displaystyle A \;=\;5000(1.0065)^5 \;\approx\;\boxed{\$5,164.63}$

Plan A (3.25% annually) is the more profitable plan.