If a bank is advertising that a new person can open an account with a 3 3/4 interest rate compounded annually and you invests $5000in an account at this rate and makes no deposits or withdrawals find the amount of money you will have to the nearest cent after three years can you give me step by step help to solving this question.Hello and thank you for posting your question to BrainmassLet the interest rate in percents be r and the initial principal X0.Let q=1+r/100 Then after one year the investment value is:X1 = X0 + X0 *r/100 = X0 * (1+r/100) = X0 * qAfter the second year:X2 = X1 + X1*r/100 = X1 * (1 + r/100) = X1 * q = (X0 * q) * q = X0 * q^2And after the third year:X3 = X2 + X2*r/100 = X2 * (1 + r/100) = X2 * q = ( X0 * q^2) * q = X0 * q^3So we can say that the value of the investment in year n is simply: Xn = X0 * q^nThis is a geometric sequence.In our case:X0 = 5000
r = 3.75
q = 1.0375
n=3X3 = X0 * q^3 = 5000 * (1.0375)^3 = $5583.86I hope it helps!
Thanks again,
Yinon




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