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Annual savings plan payment

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I have done Chapter 4, Question 64 from Brealey-Myers-Marcus, Fundamentals of Corporate Finance.

The only thing is that I have worked out question 64b, but I am unsure to which of my methods is the correct way to be doing this.

Here is the question:

A couple will retire in 50 years; they plan to spend about $30,000 a year in retirement, which should last 25 years. They believe that they can earn 8% interest per annum on retirement savings.

(a) if they make annual payments into a savings plan, how much will they need to save each year?
(b) how would the answer for part (a) change if they couple also realise that in 20 years, they will need to spend $60,000 on their child's college education.

I have attached my workings for Part (a) along with part (b) method 1 and method 2.

Could someone please advise which method is correct and why that method is correct, so that I can gain a better understanding.

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Kao-wen Peng

A couple will retire in 50 years; they plan to spend about $30,000 a year in retirement, which should last 25 years. They believe that they can ...

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