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

Brooklyn's method results in more money after 2 years

Explanation:

Compound Interest Formula

`\large \text{$ \sf A=P(1+(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+(0.03)/(4)\right)^(4 * 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+(0.05)/(12)\right)^(12 * 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.