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 Write-up

Title
Catching up in Savings

Problem Statement
Judy enters \$3000 into a savings account and decides to put \$125 in the account each month after that. The account earns 2.6% interest each year.

Five years later, her younger sister Sally places \$5000 into a savings account and puts \$150 in the account each month after that. Her account earns 4.6% interest each year.

How many years will it take until Sally has as much money in her account as Judy does in hers?

Problem setup

The easiest way to visualize the problem is in a worksheet.

Plans to Solve/Investigate the Problem

The problem can be set up on an excel worksheet.  The spreadsheet will show an opening balance, monthly deposits, and a monthly interest accrual.  In my calculation, the initial deposit was counted as month one.  Accordingly, there 11 subsequent deposits in year one for Judy and for Sally.

Investigation/Exploration of the Problem

The following is a table reflecting beginning deposits, additional deposits, and interest accrual.  It will take Sally two years and nine months to have as much money as her sister Judy.

 Judy Sally Deposits Interest Balance Deposits Interest Balance 3000 78 3078 5000 230 5230 125 83 3286 150 247 5627 125 89 3500 150 266 6043 125 94 3719 150 285 6478 125 100 3944 150 305 6933 125 106 4175 150 326 7409 125 112 4412 150 348 7907 125 118 4655 150 371 8427 125 124 4904 150 395 8972 125 131 5160 150 420 9541 125 137 5422 150 446 10137 125 144 5691 150 473 10760 125 151 5968 150 502 11412 125 158 6251 150 532 12094 125 166 6542 150 563 12807 125 173 6840 150 596 13553 125 181 7146 150 630 14334 125 189 7460 150 666 15150 125 197 7782 150 704 16004 125 206 8113 150 743 16897 125 214 8452 150 784 17831 125 223 8800 150 827 18808 125 232 9157 150 872 19830 125 241 9524 150 919 20899 125 251 9900 150 968 22017 125 261 10285 150 1020 23187 125 271 10681 150 1074 24411 125 281 11087 150 1130 25690 125 292 11503 150 1189 27029 125 302 11931 150 1250 28429 125 313 12369 150 1315 29894 125 325 12819 150 1382 31426 125 337 13280 150 1452 33029 125 349 13754 150 1526 34705 125 361 14240 150 1603 36458 125 373 14738 150 1684 38292 125 386 15250 150 1768 40210 125 400 15775 150 1857 42217 125 413 16313 150 1949 44316 125 427 16865 150 2045 46511 125 442 17432 150 2146 48808 125 456 18014 150 2252 51210 125 472 18610 150 2363 53722 125 487 19222 150 2478 56350 125 503 19850 150 2599 59099 125 519 20495 150 2725 61975 125 536 21156 150 2858 64983 125 553 21834 150 2996 68129 125 571 22530 150 3141 71420 125 589 23244 150 3292 74862 125 608 23977 125 627 24728 125 646 25499 125 666 26291 125 687 27103 125 708 27935 125 730 28790 125 752 29667 125 775 30566 125 798 31489 2 years 9 months

Extensions of the Problem

John has \$150 in his piggy bank and plans to add \$2 each week. Parneshia has \$200 in her piggy bank and plans to add \$6 each week. After how many weeks will Parneshia's bank have twice as much money as John's?

The problem can also be set up using an excel worksheet.

Author & Contact
Susan Kelly
mailto:skelly@rockdale.k12.ga.us