Your sister is the one lucky w
Your sister is the one luckywinner of the Ohio Lottery and is looking to you, as a FinanceMajor, to help out with some advice. Assuming market interest ratesare at 4.00%, on a present value basis how would you consult withher about the choice to
– take an annuity of $2,200per month for 25 years, or
– take an annuity of $2,400per month for 20 years ?
– how much is she better off by choosing the one yourecommend, remembering that more is better!
Answer:
The present value of 1st annuity will be asfollows:
Present value = Monthly payment x [ (1 – 1 / (1 +r)n) / r]
r is computed as follows:
= 4% / 12 (Since the payments are on monthly basis, hencedivided by 12)
= 0.333333%
n is computed as follows:
= 25 year x 12 months (Since the payments are on monthly basis,hence multiplied by 12)
= 300
So, the amount is computed as follows:
= $ 2,200 x [ (1 – 1 / (1 + 0.0033333)300 ) /0.0033333 ]
= $ 2,200 x 189.4524909
= $ 416,795
The present value of 2nd annuity will be asfollows:
Present value = Monthly payment x [ (1 – 1 / (1 +r)n) / r]
r is computed as follows:
= 4% / 12 (Since the payments are on monthly basis, hencedivided by 12)
= 0.333333%
n is computed as follows:
= 20 year x 12 months (Since the payments are on monthly basis,hence multiplied by 12)
= 240
So, the amount is computed as follows:
= $ 2,400 x [ (1 – 1 / (1 + 0.0033333)240 ) /0.0033333 ]
= $ 2,400 x 165.021864
= $ 396,052
So, the first annuity shall be preferred and the same isgreater than the 2nd annuity by the amount of:
= $ 416,795 – $ 396,052
= $ 20,743
Feel free to ask in case of any query relating to thisquestion
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