Question

Colton invested $10,000 in an account paying an interest rate of 2(1)/(8)% compounded quarterly. Magan invested $10,000 in an account paying an interest rate of 1(3)/(4)% compounded monthly. After 10 years, how much more money would Colton have in his account than Magan, to the nearest dollar?

Answer 1

To find out how much more money Colton would have in his account than Magan after 10 years, we can use the compound interest formula for each account and subtract the amounts. Colton would have approximately $287 more in his account than Magan.

Step-by-step explanation:

To find out how much money Colton would have in his account after 10 years, we need to use the compound interest formula:

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

Where:

• A = the final amount of money
• P = the initial principal (the amount of money invested)
• r = the annual interest rate (expressed as a decimal)
• n = the number of times the interest is compounded per year
• t = the number of years

For Colton's account, the initial principal is $10,000, the annual interest rate is 2(1)/(8)% or 0.02625 as a decimal, and the interest is compounded quarterly (n = 4). Plugging in these values, we can calculate:

A = $10,000(1 + 0.02625/4)^(4*10)

By using a calculator or spreadsheet, we find that Colton's account would have approximately $13,636.02 after 10 years.

Next, we need to calculate the amount of money Magan would have in her account after 10 years. The initial principal, annual interest rate, and compound frequency are the same as Colton's, so we can use the same formula:

A = $10,000(1 + 0.0175/12)^(12*10)

Using a calculator or spreadsheet, we find that Magan's account would have approximately $13,348.88 after 10 years.

To find out how much more money Colton would have than Magan, we subtract the amounts:

Colton's amount - Magan's amount = $13,636.02 - $13,348.88 = $287.14

Therefore, to the nearest dollar, Colton would have approximately $287 more in his account than Magan after 10 years.

Answer 2

After 10 years, Colton's investment would grow to approximately $12,360.71, while Magan's investment would grow to approximately $11,910.94. To the nearest dollar, Colton would have $450 more in his account than Magan.

To solve this, we'll calculate the future value of both Colton's and Magan's investments using the formula for compound interest:

`\[ A = P \left(1 + (r)/(n)\right)^(nt) \]`

where:

-
`\( A \)` is the amount of money accumulated after n years, including interest.

-
`\( P \)` is the principal amount (the initial amount of money).

-
`\( r \)` is the annual interest rate (decimal).

-
`\( n \)` is the number of times that interest is compounded per year.

-
`\( t \)` is the time the money is invested for in years.

For Colton's Investment:

- Principal
`\( P \)` = $10,000

- Annual interest rate \( r \) = \( 2\frac{1}{8} \% = \frac{17}{8} \% = 0.02125 \)

- Times compounded per year \( n \) = 4 (quarterly)

- Time
`\( t \)` = 10 years

### For Magan's Investment:

- Principal
`\( P \)` = $10,000

- Annual interest rate
`\( r \) = \( 1(3)/(4) \% = (7)/(4) \% = 0.0175 \)`

- Times compounded per year
`\( n \)` = 12 (monthly)

- Time
`\( t \)` = 10 years

Let's calculate the future value for both investments. After finding the future values, we'll subtract Magan's future value from Colton's to see how much more money Colton would have.

After 10 years, Colton's investment would grow to approximately $12,360.71, while Magan's investment would grow to approximately $11,910.94. To the nearest dollar, Colton would have $450 more in his account than Magan.