amadou invested $760 in an account paying an interest rate of 8\\frac{1}{2}\\% compounded continuously. mia…

amadou invested $760 in an account paying an interest rate of 8\\frac{1}{2}\\% compounded continuously. mia invested $760 in an account paying an interest rate of 8\\frac{3}{8}\\% compounded annually. after 20 years, how much more money would amadou have in his account than mia, to the nearest dollar?

amadou invested $760 in an account paying an interest rate of 8\\frac{1}{2}\\% compounded continuously. mia invested $760 in an account paying an interest rate of 8\\frac{3}{8}\\% compounded annually. after 20 years, how much more money would amadou have in his account than mia, to the nearest dollar?

Answer

Explanation:

Step1: Calculate Amadou's amount

The formula for continuous compounding is (A = Pe^{rt}). Here, (P=$760), (r = 8\frac{1}{2}%=0.085), (t = 20) years. So, (A_{1}=760\times e^{0.085\times20}). First, calculate (0.085\times20 = 1.7). Then, (e^{1.7}\approx5.473947). So, (A_{1}=760\times5.473947\approx760\times5.474 = 4160.24).

Step2: Calculate Mia's amount

The formula for annual compounding is (A=P(1 + r)^{t}). Here, (P = 760), (r=8\frac{3}{8}%=\frac{67}{8}% = 0.08375), (t = 20) years. So, (A_{2}=760\times(1 + 0.08375)^{20}). ((1+0.08375)^{20}\approx(1.08375)^{20}\approx4.7147). Then, (A_{2}=760\times4.7147\approx3583.17).

Step3: Find the difference

(A_{1}-A_{2}=4160.24 - 3583.17=577.07\approx577).

Answer:

(577)