Cameron invested $7,400 in an account paying an interest rate of 4\tfrac{3}{8}4 8 3 ​ % compounded continuously. Savannah invested $7,400 in an account paying an interest rate of 4\tfrac{3}{4}4 4 3 ​ % compounded daily. After 7 years, how much more money would Savannah have in her account than Cameron, to the nearest dollar?

$266

Step-by-step explanation:

Cameron :

r = 4 3/8% = 0.04375

P = 7400

For account compounded continuously :

A = Pe^it

i = interest ; t number of years ;

A = 7400 * e^0.04375*7

A = 7400 * e^0.30625

A = 10051.581

Savanna:

r = 4 3/4% = 0.0475

P = 7400

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

n = number of compounding times per period

A = final amount ; P = initial investment

Compounded daily :

A = 7400(1 + 0.0475/365)^365*7

A = 7400(1 + 0.0001301)^2555

A = 7400(1.0001301)^2555

A = 7400 * 1.3942879

A = 10317.731

Difference :

$(10317.731 - 10051.581)

= $266.15

= $266 (nearest dollar)