# 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!

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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