Question

Charlie Stone wants to retire in 30 years, and he wants to have an annuity of $1,000 a year for 20 years after retirement Charlie wants to receive the first annuity payment at the end of the 30th year. Using an interest rate of 10%, how much must Charlie invest today in order to have his retirement annuity (round to the nearest S10)

Answer 1

The second question is a graded question. We won't be responding to this question as per our honor code.

I will respond only to your first question

Kitty required at the time of retirement i.e. at the end of 30 years from now = PV of all the future year beginning annuities = A / r x [1 - (1 + r)^-n] x (1 + r) = 1,000 / 10% x [1 - (1 + 10%)^-20] x (1 + 10%) = $  9,365

Hence, investment required today = PV of 9,365 = 9,365 / (1 + r)^t = 9,365 / (1 + 10%)³⁰ = $  537 = $  540 (rounded to the nearest $ 10)

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The second question is a graded question. We won't be responding to this question as per our honor code.