Question

Assume you have just deposited $2100 in a bank account. Five months from today, you plan to make the first of a series of annual withdrawals from the account. Your first withdrawal will equal $250, will continue through nine years and five months from today, and will grow by 3% each. a. Set up the calculations to determine the interest rate on your account. Note: You do not need to solve anything. Just set up all equations, plug in all the numbers you would need to solve the equations, and indicate which variable you are solving for (in each equation). b. Assume that just before you make your deposit, the bank raises the interest rate on the account. Will you be able to increase or must you reduce your first withdrawal. Note: A one-word answer is sufficient!c. Assume you decide to make your final withdrawal eight years and five mo nths fro m today instead of nine years and five months from today. Will you be able to increase or must you reduce your first withdrawal (relative to your answer in b). Hint: This will reduce the number of withdrawals you make.

Answer 1

a) Let the effective interest rate per month be r

Then (assuming that after final 10th withdrawal after 9 years 5 months, balance would be 0), the equation is

2100- (250/(1+r)^5+250*1.03/(1+r)^17+250*1.03^2/(1+r)^29+.....+250*1.03^9/(1+r)^113) =0

=> (250/(1+r)^5+250*1.03/(1+r)^17+250*1.03^2/(1+r)^29+.....+250*1.03^9/(1+r)^113) = 2100

250/(1+r)^5 * (1- (1.03/(1+r)^12)^10)/(1- (1.03/(1+r)^12)) = 2100

which is the required equation where we need to solve for r .

and Interest rate on account will be = 12*r p.a.compounded monthly

b) If the bank raises the interest rates , the account will earn more interest and hence it would be possible to increase the first withdrawal

c) If final withdrawal is done eight years and five months from today instead of nine years and five months from today , there is one less less withdrawal and hence it would be possible to increase the first withdrawal