Question

Please help me im running out of time

You are trying to raise money for college. You have $1000 right now to invest into an account. You
have two options for accounts:
Option 1: An account that pays 12% interest compounded quarterly.
Option 2: An account that pays 6% interest compounded continuously.
Which option will give you the most money after 2 years? Use numerical calculations and words to

justify your answer

Answer 1

After 2 years, Option 1 will give you a larger amount of money.

To calculate the amount of money in Option 1 after 2 years, we can use the formula:

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

Where A is the end amount, P is the principal amount ($1000), r is the interest rate (12%), n is the number of times compounded in a year (4), and t is the time in years (2).

Plugging in these values, we get:

A = $1000 * (1 + 0.12/4)^(4 * 2) = $1000 * (1.03)^8 = $1000 * 1.2597 = $1259.70

To calculate the amount of money in Option 2 after 2 years, we can use the formula:

A = P * e^(rt)

Where A is the end amount, P is the principal amount ($1000), r is the interest rate (6%), and t is the time in years (2).

Plugging in these values, we get:

A = $1000 * e^(0.06 * 2) = $1000 * e^0.12 = $1000 * 1.1268 = $1126.80

So, after 2 years, the amount of money in Option 1 is $1259.70, while the amount of money in Option 2 is $1126.80. Therefore, Option 1 will give you the most money after 2 years.