You’re planning for retirement, which you want to do in 30 years. By that time,

ID: 2654652 • Letter: Y

Question

You’re planning for retirement, which you want to do in 30 years. By that time, you expect to need $3000 per month, for 20 years. You find a long-term retirement account promising a fixed 7.8% APR compounded monthly, both during the saving period, and after beginning withdrawals. (You can’t begin withdrawing money from it prior to 30 years without penalty.)

A. To have enough to fund your withdrawals, how much will you have need to save by then?

B. In order to accumulate enough to retire, you begin monthly deposits into the account now. How much will you need to set aside each month to reach your retirement goal?

C. How much interest will have been earned overall, after the last withdrawal is made?

D. Assuming the same annual rate of inflation of 2.45% over the next 30 years, how much would that $3000 be worth in today’s money (i.e. what would the purchasing power be during the first year of retirement)?

Explanation / Answer

Part-A

Without considering inflation during the 20 years of retirement

We need to save: $3,000*12*20 = $720,000

By considering an inflation of 2.45% for the 20 years during retirement

We need to save $914,993

But with the interest of 7.8% compounded, the retirement corpus required will be $474,683

Part- B

A monthly saving of $336 is required for this. (Show in Table)

Part –C

Total Ineterst earned after the withdrawal of last installment is$ 816,465

Part –D

In today’s terms the value of $3,000 would be $1,451.32 :

$3,000/(1.0245)^30 =$1,451.32

Table (Working)

Growth of

Total Corpus

corpus avail.

Monthly

future

amt. inv.

accumulated

for annuity

Year

invest.

Expenses

mon. inv.

so far

(year-end)

(year-start)

1451

336

1487

4346

336

1523

9032

336

1561

14082

336

1599

19527

336

1638

25397

336

1678

31724

336

1719

38545

336

1761

45898

336

1805

53824

336

1849

62369

336

1894

71580

336

1940

81509

336

1988

92213

336

2037

103752

336

2087

116191

336

2138

129601

336

2190

144056

336

2244

159638

336

2299

176437

336

2355

194545

336

2413

214066

336

2472

235109

336

2532

257794

336

2595

282248

336

2658

308610

336

2723

337028

336

2790

367662

336

2858

400686

336

2928

436286

Interest ernd.

336

3000

474663

474663

during wdl.

Interest End. Inv.

3074

471927

437780

34147

353703

3149

468004

434141

33863

3226

462777

429292

33485

3305

456120

423117

33003

3386

447896

415488

32408

3469

437957

406268

31689

3554

426144

395309

30834

3641

412282

382451

29831

3730

396186

367520

28667

3822

377652

350327

27325

3915

356461

330669

25792

4011

332377

308327

24050

4109

305142

283063

22079

4210

274481

254621

19860

4313

240094

222722

17372

4419

201658

187067

14591

4527

158823

147331

11492

4638

111213

103166

8047

4752

58418

54191

4227

4868

Total Int. earned

816465