Alin, a 45-year-old librarian, 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 an RRSP that invested in the bond market. The manager at his local bank assured him that the RRSP he chose would generate returns of 8% compounded quarterly. Alin learned Mathematics of Finance during his college days to be a well-informed investor and knew the right questions to ask the bank manager. What answers would the bank manager provide Alin for the following questions?

a. How long (rounded up to the next month) will it take for an investment to double while earning interest at the offered rate of 8% compounded quarterly?

b. If the offered rate was compounded daily instead of quarterly, how long (rounded up to the next month) would it take for an investment to double?

c. Alin 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.

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

e. What is the effective rate of the monthly compounded rate calculated in part (d)?

f. He wanted to know if investing his money at 8% compounded monthly or at 8% compounded semi-annually would give him a higher accumulated value than the offered rate at the end of the same time period. Provide a suitable example with calculations to demonstrate the manager's approach to answering his question.

g. If he wants to withdraw an amount equal to 50% of the original amount invested at the end of 5 years and another amount equal to 50% of the original amount invested at the end of 10 years, what percent of his original investment would be available for withdrawal at the end of 15 years?

h. If he would like to make a deposit equal to 25% of the original investment in 5 years and another deposit equal to 75% of the original investment in 10 years, what percent of his original investment would be available for withdrawal at the end of 15 years?