Question

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You are planning to make 18 monthly withdrawals beginning at the end of the sixth month. You plan to withdraw $116 in the sixth month and increase your withdrawals by $10 over the previous month's withdrawal. How much should you deposit now in a bank account that pays 12% per year compounded monthly? Enter the answer with two decimal places. Do not enter the dollar (S) symbol. eg. 1234.56 Hint: Determine m and k and use the decision tree to find how you must setup Remember to bring all the cash flows to the proper time period required to answer this question the cash flow equation.

Answer 1

ANSWER:

I = 12% per year or 12% / 12 = 1% per month

n = 18

initial withdrawal = $116

increase in deposit = $10

pw = deposit in 6th month(p/f,i,n) + deposit in 7th month(p/f,i,n) + deposit in 8th month(p/f,i,n) + deposit in 9th month(p/f,i,n) + deposit in 10th month(p/f,i,n) + deposit in 11th month(p/f,i,n) + deposit in 12th month(p/f,i,n) + deposit in 13th month(p/f,i,n) + deposit in 14th month(p/f,i,n) + deposit in 15th month(p/f,i,n) + deposit in 16th month(p/f,i,n) + deposit in 17th month(p/f,i,n) + deposit in 18th month(p/f,i,n) + deposit in 19th month(p/f,i,n) + deposit in 20th month(p/f,i,n) + deposit in 21th month(p/f,i,n) + deposit in 22th month(p/f,i,n) + deposit in 23th month(p/f,i,n)

pw = 116(p/f,1%,6) + 126(p/f,1%,7) + 136(p/f,1%,8) + 146(p/f,1%,9) + 156(p/f,1%,10) + 166(p/f,1%,11) + 176(p/f,1%,12) + 186(p/f,1%,13) + 196(p/f,1%,14) + 206(p/f,1%,15) + 216(p/f,1%,16) + 226(p/f,1%,17) + 236(p/f,1%,18) + 246(p/f,1%,19) + 256(p/f,1%,20) + 266(p/f,1%,21) + 276(p/f,1%,22) + 286(p/f,1%,23)

pw = 116 * .942 + 126 * 0.9327 + 136 * 0.9235 + 146 * 0.9143 + 156 * 0.9053 + 166 * 0.8963 + 176 * 0.8874 + 186 * 0.8787 + 196 * 0.87 + 206 * 0.8613 + 216 * 0.8528 + 226 * 0.8444 + 236 * 0.836 + 246 * 0.8277 + 256 * 0.8195 + 266 * 0.8114 + 276 * 0.8034 + 286 * 0.7954

pw = 109.272 + 117.5202 + 125.596 + 133.4878 + 141.2268 + 148.7858 + 156.1824 + 163.4382 + 170.52 + 177.4278 + 184.2048 + 190.8344 + 197.296 + 203.6142 + 209.792 + 215.8324 + 221.7384 + 227.4844

pw = 3094.254

so the amount that needs to be deposited is $3,094.254