a$)$ You deposit $$1,000$ into your bank account. If the bank pays $4\%$ interest per annum, how much will you accumulate in your account at the end of $10$th year?

b$)$ You will require $$700$ in $5$ years. If you earn $5\%$ interest on your funds, how much will you need to invest today in order to reach your savings goal?

c$)$ You deposited $$10,000$ in your back account $5$ year ago and you now noticed that it has increased to $$20,000.$ What is the implied interest rate provided by your bank?

d$)$ What is the present value of a $10-$year ordinary annuity of $$5000$ if the discount rate is $7\%?$

e$)$ Consider a $4-$year amortizing loan. You borrow $$10,000$ initially and repay it in $4$ equal annual year$-$end payments and the interest rate is $10\%.$

What will be the annual payment?

Prepare the loan amortization schedule.

f$)$ You are working as a financial planner. A couple has asked you to put together an investment plan for the education of their daughter Sophie. She is a bright seven$-$yearold $($her birthday is today$),$ and everyone hopes she will go to university after high school in $10$ years, on her $17$th birthday. You estimate that today the cost of a year of university is $$16,000,$ including the cost of tuition, books, accommodation, food, and clothing. You forecast that the annual inflation rate will be $3\%.$ You may assume that these costs are incurred at the start of each university year. A typical university program lasts $4$ years. The effective annual nominal interest rate is $5\%.$ Suppose the couple invests money on her birthday, starting today and ending one year before she starts university. How much must they invest each year to have money to send their daughter to university?

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