Question

In: Finance

I am trying to start saving for retirement. I am investing all my cash into the...

I am trying to start saving for retirement. I am investing all my cash into the S&P 500, which will assume consistently 9.8% interest, compounded annually. I initially put a lump sum of $100 into my account, and I will deposit $10 every second week.

a) After 10 years, how much money will I have invested?

b) After 10 years, if I sold all of my stocks, how much money will I have in my account?

c) After 25 years, how much money have I invested?

d) If I had not sold my stocks at the 10 year mark and instead held onto them an additional 15 years before selling, how much additional money would I have in my account?

Solutions

Expert Solution

(a)

Assuming there are 52.1429 weeks in a year

Total lump sum investment =$100

Total weeks in 10 years = 10*52.1429 = 521.429 weeks

$10 deposits take place every second week

Total 2-weekly deposits over 10 years = $10 * 521.429/2 = $2607.145

Total money invested in 10 years = lump sum investment + Total 2-weekly deposits

Total money invested in 10 years = $100+$2607.145 = $2707.145

(b)

We use a financial calculator function FV for this. We input the following

PV = -100 (lump-sum investment)

PMT = -10 ( 2-weekly deposits)

N = 521.429/2 ( Total number of 2-weekly deposits over 10 years)

I/Y = 9.8/(54.1429/2) = 0.362005 ( Compounding is done every 2-weeks and 9.8% is the annual rate)

CPT FV, we get

FV = $4580.65

Hence, after 10 years $4580.65 will be there in the account

(c)

Assuming there are 52.1429 weeks in a year

Total lump sum investment =$100

Total weeks in 25years = 25*52.1429 = 1303.5725 weeks

$10 deposits take place every second week

Total 2-weekly deposits over 25 years = $10 * 1303.5725 /2 = $6517.8625

Total money invested in 25years = lump sum investment + Total 2-weekly deposits

Total money invested in 25 years = $100+$6517.8625= $6617.8625

(d)

Case 1: If he stops investing for additional 15 years

Value of stock at 10-year mark = $4580.65

Total Value of $4580.65 after additional 15 years = 4580.65* (1+0.098)^15

Total value of $4580.65 after additional 15 years = $ 18619.2511

Additional money = Total Value of $4580.65 after additional 15 years - Value of stock at 10-year mark

Additional money = $ 18619.2511 - $4580.65 = $14,038.601

Case 2: He keeps on investing for an additional 15 years

We find the FV after 15 additional years or total of 25 years

PV = -100 (lump-sum investment)

PMT = -10 ( 2-weekly deposits)

N = 1303.5725 /2 ( Total number of 2-weekly deposits over 10 years)

I/Y = 9.8/(54.1429/2) = 0.362005 ( Compounding is done every 2-weeks and 9.8% is the annual rate)

CPT FV, we get

FV after 25 years= $27409.060

Additional money = Total Value of after 25 years( including additional investments) - Value of stock at the 10-year mark

Additional money =$27409.060 - $4580.65 = $22,828.41

jeff jeffy answered 1 year ago

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