Question

Q1) You invest $4,186 at the beginning of every year and your friend invests $4,186 at the end of every year. If you both earn an annual rate of return of 13.00%. a) how much will you have in your account after 32 years? b) How much will your friend have in his account?

Answer 1

Annuity = A = 4186

Interest = i = 13%

Discount factor = d = i/(1+i) = .13/1.13 = 0.115044

Period = n = 32 years

1) For my cases, it is annuity due since payments are made at the beginning of the year.

FV = A x [(1+i)³² - 1 ]/d = 4186 x [1.13³² -1 ]/0.115044 = 1780992.65 ( approx value)

2) For my friend's case it is normal annuity :

FV = A x [(1+i)³² - 1 ]/i = 4186 x [1.13³² -1 ]/0.13 = 1576096.30

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