This is a question from TJC Promotion 2017 Question 10. Thank you Mr. Wee for sharing.

Mr. Scrimp started a savings account which pays compound interest at a rate of r% per year on the last day of each year.

He made an initial deposit of latex x at the start of each year.

(i) Show that the total amount in the savings account at the end of the n year is latex \frac{k}{k-1} (k^n – 1)x latex k = \frac{100 + r}{100} in the savings account. Find the value of , giving your answer correct to one decimal place.

Assume that the last deposit is made on 1 January 2019 and that the total amount in the savings account is latex Nlatex 1 \le N \le 202000 and a year-end profit of 20 more profit that in the previous year.

(iii) Find the total amount Mr. Scrimp will have at the end of years if he invests in the financial product.

(iv) Using the value of found in (ii), find the maximum number of years Mr. Scrimp should invest in the financial product for it to be more profitable than keeping the money in the savings account.

(i)

Let

Total Amount

(ii)

Using GC,

(1 decimal place)

(iii)

Total amount

(iv)

With the savings account, he has latex [50000(1.009)^N]latex N at the end of years.

For it to be more profitable,