Question

1.

1. Compare the proceeds from a 2-year $100,000 investment at 5.5%, annual compounding, with that from investing for 1 year at 5.5% and rolling over at 5.5% for the second year.
2. Compare the proceeds from a 2-week (money market) $100,000 investment at 5.5%, with that from investing for 1 week at 5.5% and rolling over at 5.5% for the second week.

2.

1. You put 100,000 into a money market instrument September 4 2018 for six calendar months at 3%. When it matures, you roll it over for the next six months at 4%. What are the proceeds? Be careful with the day counts.
2. What would need to be the (“equivalent”) rate on a one-year (i.e., non-money market) semi-annual compounding instrument in order to produce the same proceeds?
3. Suppose the one-year rate in b) is 3.5%. What must the latter (forward) 6-month rate be in a), where the initial rate is 3%, in order to produce the same proceeds as the one-year?

3. You invested $1mm on Sept 4, a Friday, for three days at 1%. Because Monday is Labor Day, you will not receive your proceeds until the next day. What is your “effective” rate (the annualized rate you “really” received)?

Answer 1

Hello

As per HOMEWORKLIB RULES, one is only supposed to answer the first question in case of multiple questions.

Solving part (a) of Question 1 -

Option I is the two year investment at 5.5% annual compounding.

Option II is the investment at 5.5% for 1 year will roll on at 5.5%

As we see, no change in the returns as the re-investment rate in year 2 is the same as year 1. which also means that both the options are invested at a annual compound rate of 5.5%.

Solving part (b) of Question 1 -

Option I - Two week at 5.5%

Option II - One week at 5.5% and second week roll over at 5.5%

We can see the difference in the returns here, because in Option I - the returns were invested at simple interest rate for 2 weeks straight. And in Option II - returns were compounded weekly after week 1 at 5.5%.

Hope this helps

Thank you.