2020 HCI Promo Q10

John's annual income was \(\$80000\) in 2009 and he spent all his income in that year. In the next \(10\) years, his salary increased by \(\$5500\) per year, but inflation caused his expenditure to rise by \(3\%\) from his expenditure in the previous year. Show that his expenditure in 2011 was \(\$84872\).[1]

Assuming that John kept the remaining amount of his income after expenditure as savings each year, find the total amount of money that John saved by the end of 2019, giving your answer correct to the nearest dollar.[4]

At the start of 2020, due to the Covid-19 situation, there was no more increment in John’s salary. Instead, as a member of the senior management team in his company, John accepted a \(20\%\) reduction in pay to help his company. Assuming that John would be paid equally for all \(12\) months in 2020, find John's monthly salary in 2020.[2]

As the economy is uncertain in 2020, John decided to cut down on his expenditure and started a new savings account. On 1st January 2020, John put \(\$500\) into the savings account, and on the first day of each subsequent month, he would put another \(\$500\) into the account. The interest at a rate of \(0.25\%\) per month, is calculated and added to the account on the last day of each month.

Show that the amount of money in John's account on the last day of the \({{n}^{\mathrm{th}}}\) month is given by \(t\left( {{1.0025}^{n}}-1 \right)\), where \(t\) is a constant to be determined.

Hence, find the month and year in which the amount of money in John's account first exceeds \(\$10000\). Explain whether this occurs on the first day or last day of the month.[5]