Question

Suppose you invest $200 per month for a period of 30 years.

a) How much money would you have at the end of the 30-year period, assuming that the yearly interest rate is 12% compounded monthly? You can assume that the payments are deposited at the end of each month. (Hint: write the amount accumulated in the bank for the first few months, and try to get a pattern out of that.) (answer: $698,992.83)

b) Using the same approach, indicate how much you would have at the end of 35 years? (answer: $1,286,191.83)

A pool maintenance worker puts 0.1 ppm of chlorine in a pool each day, at the end of the day.

a) Assuming that initially, the pool contained 3 ppm of chlorine and that chlorine dissipates at a rate of 15% per day, find the level of chlorine in the pool, in the long run. (answer: 0.67)

b) If it is given that the ideal chlorine level in a pool is 2.5 ppm, what would you advise the pool worker in terms of the amount he should be adding each day? (answer: 0.375)

Answer 1

Given, monthly deposit = $ 200

Interest rate = 12% = 1% per month

Time = 30 years = 30 × 12 = 360 months

A. The future value of the deposit will be

Now, calculating for 35 years = 420 months

2. Everyday an additional 0.1 ppm of chlorine is added. Thus, the amount of chlorine in the long run will be

0.1/0.15 = 0.6666 = 0.67

B. In the long run an amount of 2.5 ppm chlorine has to be maintained this is possible when

2.5 = i/0.15

=> i = 2.5 × 0.15 = 0.375

Please contact of having any query will be obliged to you for your generous support. Your help mean a lot to me, please help. Thank you.