1. a. Steve Hitchcock is 43 years old today and he wishes to accumulate $469,000

ID: 2558365 • Letter: 1

Question

1.
a. Steve Hitchcock is 43 years old today and he wishes to accumulate $469,000 by his 67th birthday so he can retire to his summer place on Lake Hopatcong. He wishes to accumulate this amount by making equal deposits on his 43th through his 66th birthdays. What annual deposit must Steve make if the fund will earn 12% interest compounded annually?
b. Cindy Ross has $20,200 to invest today at 12% to pay a debt of $62,738. How many years will it take her to accumulate enough to liquidate the debt?

Explanation / Answer

Answer

Answer may vary slightly due to rounding off

Total years from 43rd birthday to 66th birthday = 24

PV for 25th year at 12% = [(1/(1.12)25] = 0.05882

PV of $469000 at 25th year = $469,000 x 0.05882 = $27,588.13

PV Annuity Factor for 24 years at 12% = 7.784315

Amount to be deposited each year will be 27588.13/7.784315 = $3544

Verification:

Years

Opening Balances + $3544 deposit each year

Interest @ 12%

Closing Balance (including Interest)

3544

425

3969

7513

902

8415

11959

1435

13394

16938

2033

18971

22515

2702

25217

28761

3451

32212

35756

4291

40047

43591

5231

48822

52366

6284

58650

62194

7463

69657

73201

8784

81985

85529

10264

95793

99337

11920

111257

114802

13776

128578

132122

15855

147976

151520

18182

169703

173247

20790

194037

197581

23710

221290

224834

26980

251815

255359

30643

286002

289546

34745

324291

327835

39340

367176

370720

44486

415206

418750

50250

$469000

Hence, proved that at the end of 24th year, amount matured will be $469,000

Year

Opening Investment balance (A)

Interest earned at 12% (B = A x 12%)

Ending Investment balance (C=A+B)

20200

2424

22624

2715

25339

3041

28380

3406

31785

3814

35599

4272

39871

4785

44656

5359

50014

6002

56016

6722

$62,738

Hence, at the end if 10 year, the investment will yield $62,738 at an interest rate of 12%