Question

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.

Please show solve by hand

Answer 1

Answer :

a) 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.

Option 1: Proceeds from a 2-year $100,000 investment at 5.5%, annual compounding =

=P + P(1 + r)^T

= 100,000 + 100,000(1+0.055)²

=111,302.50

Option II : Investing for 1 year at 5.5% and rolling over at 5.5% for the second year =

Interest for Ist year = 100,000*5.5% = 5500

Amount at the end of Ist Year = 100,000 + 5500 = 105,500

Rolling over to 2nd year, we get

Interest = 105,500*5.5% = 5802.50

Total amount at the end of year 2 = 105,500 + 5802.50 = 111,302.50

So, we can see that there is no difference and there is 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%.

Part b) 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.

Solution: Similarly we can make calculations in this part as follows:

Option 1: Proceeds from a 2-week $100,000 investment at 5.5% =

Interest = 100,000 * 5.5%* 2/52 = 211.54

Total amount = 100,000 + 211.54 = 100,211.54

Option II : Investing for 1st week at 5.5% and rolling over at 5.5% for the second week =

Interest for Ist year = 100,000*5.5%*1/52 = 105.77

Amount at the end of Ist week = 100,000 + 105.77 = 100,105.77

Rolling over to 2nd week, we get

Interest = 100,105.77*5.5%*1/52 = 105.88

Total amount at the end of year 2 = 100,105.77 + 105.88 = 100,211.65

So, we can see that there is minor difference (100,211.65 - 100211.54) in the two options in this part because in option 1 interest is simple interest (100,211.54) and in option 2 interest is rolled over, means it is compound interest(100,211.65)