Question

This is a classic retirement problem. A friend is celebrating her birthday and wants to start saving for her anticipated retirement. She has the following years to retirement and retirement spending goals:

Years until retirement	35
Amount to withdraw each year	$85,000
Years to withdraw in retirement	25
Interest rate	7.5%

Because your friend is planning ahead, the first withdrawal will not take place until one year after she retires. She wants to make equal annual deposits into her account for her retirement fund.

a) If she starts making these deposits in one year and makes her last deposit on the day she retires, what amount must she deposit annually to be able to make the desired withdrawals at retirement?

b) Suppose your friend just inherited a large sum of money. Rather than making equal annual payments, she decided to make one lump-sum deposit today to cover her retirement needs. What amount does she have to deposit today?

c) Suppose your friend's employer will contribute to the account each year as part of the company's profit-sharing plan. In addition, your friend expects a distribution from a family trust several years from now. What amount must she deposit annually now to be able to make the desired withdrawals at retirement?

Employer’s annual contribution	$1,300
Years until trust fund distribution	15
Amount of trust fund distribution	$20,000

Please show steps for full credit.

Answer 1

Employer = $1300 Contribution truet fund e $20000, n=15 the imao na FV of Employer contribution for 25 years = 1300 ((1.075351) 0.075 (1075)-1) = 200527.087 ->

after is years she get funds from trust 20,000$ which get compounded for 20 years @ 7.sp FV = 20000 (1075) 20 = 84954. ~ ♡ Amount needed for retirement = 947490.39 Subtract 3f 4 from 947490.39 = 66 2006:303 FV annuity of monthly deposit let be se Should equal to 662006.303 (C1-0403 3-1) 662006303 0.075 x=4291734

Pv of retirement fun PV pvom (n-Goma) mm - 3.5000 = n=25 r=7.54. Pmi=85000 = 947490.39 > 0 FV of amount she deposit each month let it be a n=35 FV = r=7.54. v= f ((1+r)^-1) [2=754. Equalate Of ® uffind & 2 (+8) 2-1) = 947490.39 I ((1.075)36-1) - 949490:39 ge=6142.49 6 set the amount inherited be y Y (1+0.075) S = 947490.39 00 L Y-75, 383