Question

Patrick and Brooklyn are making decisions about their bank accounts. Patrick wants to deposit $300 as a principal amount, with an interest of 3% compounded quarterly. Brooklyn wants to deposit $300 as the principal amount, with an interest of 5% compounded monthly. Explain which method results in more money after 2 years. Show all work.

Answer 1

Answer:

Brooklyn's method results in more money after 2 years

Step-by-step explanation:

Compound Interest Formula

$\large \text{ \sf A=P(1+\frac{r}{n})^{nt} }$

where:

• A = final amount
• P = principal amount
• r = interest rate (in decimal form)
• n = number of times interest applied per time period
• t = number of time periods elapsed

Patrick's Method

Given:

• P = $300
• r = 3% = 0.03
• n = 4
• t = 2

Substituting the given values into the formula and solving for A:

$\implies \sf A=300\left(1+\dfrac{0.03}{4}\right)^{4 \times 2}$

$\implies \sf A=300\left(1.0075\right)^{8}$

$\implies \sf A=318.4796543...$

Therefore, using Patrick's method, there would be $318.48 in the account after 2 years.

Brooklyn's Method

Given:

• P = $300
• r = 5% = 0.05
• n = 12
• t = 2

Substituting the given values into the formula and solving for A:

$\implies \sf A=300\left(1+\dfrac{0.05}{12}\right)^{12 \times 2}$

$\implies \sf A=331.4824007...$

Therefore, using Brooklyn's method, there would be $331.48 in the account after 2 years.

As $331.48 > $318.48 then Brooklyn's method results in more money after 2 years.