Question

um help?
Patrick and Brooklyn are making decisions about their bank accounts. Patrick wants to deposit $300 as 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 will have more money after two years

She'll have 13 more dollars compared to Patrick.

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Explanation:

We'll be using this compound interest formula

A = P*(1+r/n)^(n*t)

The variables are:

• A = final amount at time t
• P = initial amount, aka deposit or principal
• r = decimal form of the annual interest rate
• n = number of times we compound the money per year
• t = number of years

Patrick has the following values:

• P = 300
• r = 0.03
• n = 4
• t = 2

which leads to...

A = P*(1+r/n)^(n*t)

A = 300*(1+0.03/4)^(4*2)

A = 318.479654345482

A = 318.48

Patrick will have $318.48 in his account after 2 years.

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For Brooklyn, she has:

• P = 300
• r = 0.05
• n = 12
• t = 2

Those values then plug into the formula to get...

A = P*(1+r/n)^(n*t)

A = 300*(1+0.05/12)^(12*2)

A = 331.482400667499

A = 331.48

Brooklyn will have $331.48 in her account after 2 years.

We can see that Brooklyn earns more compared to Patrick.

She has $331.48 - $318.48 = 13 more dollars compared to Patrick.

This is to be expected for two reasons:

1. Her annual interest rate is higher (5% compared to 3%)
2. The money in her account is compounded more frequently (12 times per year compared to 4 times per year)