Question

Gabriel invested $900 in an account paying an interest rate of 3 1/4 % compounded daily. Daniel invested $900 in an account paying an interest rate of 3 3/8 % compounded continuously. After 19 years, how much more money would Daniel have in his account than Gabriel, to the nearest dollar?

Answer 1

Answer:

$40

Step-by-step explanation:

The earnings of Gabriel can be calculated with the formula:

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

Where P = 900, r = 0.0325, n = 365 and t = 19

So we have:

P = 900 * (1 + 0.0325/365)^(365*19) = $1,668.81

The earnings of Daniel can be calculated with the formula:

P = Po * e^(rt)

Where Po = 900, r = 0.03375 and t = 19

So we have:

P = 900 * e^(0.03375*19) = $1,708.97

So the amount that Daniel will have more than Gabriel is:

1708.97 - 1668.81 = $40.16

Rounding to nearest dollar, the difference is $40