Question

Jane is investing in a stock.She puts in $100. Every week , this stock rises by 30% but every other week, the stock lowers by 11%. At the 6th week, she takes out half the money out of the stock to buy a watch. On week 9, she adds $100 to the stock. At what point does her investment reach $6,000?

Answer 1

Answer: Jane’s investment reaches $6,000 by the end of week 14

Explanation: To solve this problem, we need to use the compound interest formula:

A = P (1 + r/n)^nt

Where:

A = future value of the investment

P = principal amount

r = annual interest rate (decimal)

n = number of times interest is compounded per year

t = time in years

We can assume that the stock is compounded weekly, so n = 52. We also need to convert the percentage changes to decimals, so 30% = 0.3 and 11% = 0.11.

We can divide the problem into three phases:

Phase 1: From week 1 to week 6, Jane invests $100 and the stock alternates between rising by 30% and lowering by 11%. The effective weekly interest rate for this phase is (1 + 0.3) * (1 - 0.11) - 1 = 0.157, or 15.7%. The future value at the end of week 6 is:

A = 100 * (1 + 0.157/52)^(52 * 6/52) A = $197.66

Phase 2: At the end of week 6, Jane takes out half of the money, so she has $98.83 left in the stock. From week 7 to week 9, the stock continues to alternate between rising by 30% and lowering by 11%. The effective weekly interest rate for this phase is the same as before, 15.7%. The future value at the end of week 9 is:

A = 98.83 * (1 + 0.157/52)^(52 * 3/52) A = $193.66

Phase 3: At the end of week 9, Jane adds $100 to the stock, so she has $293.66 in the stock. From week 10 to week 14, the stock continues to alternate between rising by 30% and lowering by 11%. The effective weekly interest rate for this phase is the same as before, 15.7%. The future value at the end of week 14 is:

A = 293.66 * (1 + 0.157/52)^(52 * 5/52) A = $6018.77

Therefore, Jane’s investment reaches $6,000 at the end of week 14.

Hope this helps, and have a great day! =)