Question

Consider Donald and Joe who are both 30 years of age and recently graduated with a degree in Finance. Both Donald and Joe plan to retire at age 67, and the retirement plan pays a 12 percent per annum return and is also compounded monthly. Donald plans to invest $1,000 per month beginning next month into his retirement account, while Joe shall invest $2,000 per month. Joe however does not plan to begin investing until 10 years after Donald begins to invest. How much will each of the newly grads have at retirement?

Answer 1

The present age of both Donal and Joe is 30 Yrs

Retirement age = 67

So investment period = 67-30 = 37 years .

So Donald will save for 37*12 – 1 = 443 months

Joe will save for = 27*12 - 1 = 323 months

So

The FV of the savings annuity is given by

FV= PMT *( (1+r)^n-1/r)

Here PMT = payment per period

R = ROI

N = periods

So

So the retirements amounts are

DONALD

FV = (1000 * ((1+ 0.12/12)^443 -1 /) 0.12/12 ) = $ 8,110,480.72

JOE

FV= (2000 * ((1+ 0.12/12)^323 -1 /) 0.12/12 ) = $ 4,775,465.60

Thanks