CASE A $-$ INVESTING FOR THE FUTURE

Sebastian, a $45-$year$-$old shoe salesman, decided that it was time he started saving for retirement. He had money in his chequing account that was earning $1\%$ compounded annually, and he decided to transfer this amount into a Registered Retirement Savings Plan $($RRSP$)$ that invested in the bond market. The manager at his local bank assured him that the RRSP he chose would generate returns of $9\mathrm{.}027\%$ compounded quarterly. Sebastian learned mathematics of finance during his college days to be a wellinformed investor and knew the right questions to ask the bank manager. What answers would the bank manager provide Sebastian for the following questions?

Assume a PV for your calculations.

How long $($in years and months, rounded up to the next month$)$ will it take for an investment to double while earning interest at the offered rate of $9\mathrm{.}027\%$ compounded quarterly?

What is the effective interest rate of the offered nominal rate?

If the offered rate dvas compounded daily instead of quarterly, how long $($in years and months, rounded up to the next month$)$ would it take for an investment to double?

Sebastian wanted to triple his original investment in the RRSP before his retirement in $15$ years. Is this achievable at the offered rate? Support your answer with an example.

At what rate compounded monthly would his investment triple in $15$ years?

If he would like to make a deposit equal to $35\%$ of the original investment in $5$ years and another deposit equal to $63\%$ of the original investment in $10$ years, what percent of his original investment would be available for withdrawal at the end of $15$ years?