Suppose A dollars is deposited in a bank that pays interest at the rate of rp pe

Question

Suppose A dollars is deposited in a bank that pays interest at the rate of rp per period and that at the end of each period additional deposits of b dollars are made. Write a difference equation for the amount in the bank at the end of the nth period, just after the deposit, and show that the solution is where a Also how much would be accumulated after 10 years if an initial deposit of Si00 dollars is made and 10 dollars is deposited each month. Assume that the bank pays 8% interest compounded monthly.

Explanation / Answer

initial deposite A after 1st period, interest = Arp, another deposit b,total money x1 = A + Arp + b = Aa + b after 2nd period, interest = (Aa + b)rp, another depositb, total money x2 = Aa + b + (Aa + b)rp + b = (Aa +b)(1 + rp) + b = a(Aa + b) + b = Aa2 + b(1 +a) after 3rd period, x3 = Aa3 + b(1 + a + a2) .... xn = Aan + b(1 + a + a2 + ... +an-1) = Aan + b(1 - an)/(1 -a) A = $100, rp = 8%/12, a = 1.006667, b = $10, n = 10*12 =120 x120 = $2051.42

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