Question

Please solve this for me step by step (no excel, no financial cal. show algebra)? Thank you.

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?

Answer 1

a. interest earned for first 6 months at 3% = 100000*.03*0.5 = 1,500

now you have = 100,000 +1,500 = 101,500

interest earned on 101,500 for 6 months at 4% = 101,500*.04*0.5 = 2,030

final proceeds after 1 year = 101,500 + 2,030 = $103,530

b. Compounding formula:

here A = $103,530

P = $100,000

n = 2 (two semi-annual in one year)

103530 = 100000(1+r/2)²

(1+r/2)² = 103530/100000 = 1.0353

1+r/2 = 1.0175

r/2 = 0.0175

r = 0.035

therefore at 3.5% per annum semi - annual compounding we get same proceeds as part one.

c. As already seen in part a) and b) when the one year rate in part b) is 3.5% and initial 6-month rate be in a) is 3% in order to get same proceeds the later rate in part a should be 4%