2025 MI PU1 Promo Q6

A fresh graduate is offered a job with a monthly salary of \(\$\)3000. Her contract states that she will receive an annual increment of \(\$\)160 to her monthly salary, effective at the start of each new year. For example, she earns \(\$\)3000 per month in her first year and \(\$\)3160 per month in her second year, and so on.

She plans to save 20% of her monthly salary every month. Let \(T_n\) denotes the total amount of money saved in the \(n\)th year where \(n=1,2,3,4,5\).

1. Find \(T_1\), \(T_2\) and show that \(T_3\) is 7968.[2]
2. Find the total amount that she will save over 5 complete years.[2]

Let \(n\) be the number of complete years from the start of her employment.

4. Find the smallest value of \(n\) such that her total accumulated savings exceed $100000.[3]