Intermath | Workshop Support

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

Additional Investigations:  Piggy Savings

 

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