Chegg, I am having trouble with this question. Please help me out by showing how

Question

Chegg, I am having trouble with this question. Please help me out by showing how you arrive at the answer for the 2 questions that are highlighted in bold by showing your work (step by step). The more work that you show, it would better help me understand the problem and how to approach it in the future. This question is important to me because I need it for an assignment. Please help me out. Thanks.

We want to retire in 30 years, and we shall need $50,000 income per annum during our retirement which will last 20 years. We can save $10,000 annually during the first 10 years. We estimate that from year 16 till 20 we shall return to school for a graduate degree, which will cost $40,000 yearly in actual cash flow and opportunity cost expenses. Additionally, we’ll send our niece to college for 4 years starting in year 26 from now. Her tuition is $15,000 and will rise by 4% annually, but it will be the same every year after year 26. First, We would like to know what the pension fund should be to finance our retirement. Second, what annual savings should we accumulate from years 30 to 40 to be able to fund all the aforementioned expenses and our retirement. We have a discount rate of 6%.

Explanation / Answer

Solution :-

Forstly lets calculate the amount of Pension fund you would need at the end of 30 years

PV of an Annuity = R ×{( 1 (1 + i)-n)/i}

where

i is the interest rate per compounding period;

   n are the number of compounding periods; and

   R is the fixed periodic payment.

now applying this formula i = 6%, n = 20 years, R = $50000

therefore at the end of 2046 you would require pension fund of $ 573,496

Secondly though question is not clear on the years since in the first sentence it is said that you need $50000 after 30 years & then in the second part you are saying that what savings you want from year 30 - 40 ?? really confusing

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