To calculate the future values of Colton and Magan's investments after 10 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for
Let's calculate Colton's future value first:
P_Colton = $10,000
r_Colton = 21% or 0.21
n_Colton = 4 (compounded quarterly)
t_Colton = 10 years
A_Colton = 10000(1 + 0.21/4)^(4*10)
A_Colton ≈ $31,723.85 (rounded to the nearest cent)
Now, let's calculate Magan's future value:
P_Magan = $10,000
r_Magan = 13% or 0.13 (1/3% compounded monthly)
n_Magan = 12 (compounded monthly)
t_Magan = 10 years
A_Magan = 10000(1 + 0.13/12)^(12*10)
A_Magan ≈ $23,828.56 (rounded to the nearest cent)
Now, to find out how much more money Colton would have than Magan after 10 years:
Difference = A_Colton - A_Magan
Difference ≈ $31,723.85 - $23,828.56
Difference ≈ $7,895.29
So, to the nearest dollar, Colton would have approximately $7,895 more in his account than Magan after 10 years.