Question

2. You make an initial deposit of P dollars into each of two accounts with different schemes: Account 1: The account earns interest at a rate of r monthly for the first six months, and then s monthly for the next six months, then the pattern repeats. Account 2: The account earns interest at a rate of r in the first month, s in the second month, then the pattern repeats. (i) Compute the value of Account 1 after 3 years. Clearly indicate your reasoning, and explain your answer. (ii) Compute the value of Account 2 after 3 years. Clearly indicate your reasoning, and explain your answer. (iii) What is the relationship between your answers in parts (a) and (b)? Explain your answer. Your explanation can justify the mathematical relationship or financial relationship, but you do not need to do both.

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Answer 1

jy } Time (in months) Account I has earned interest at sate of 'g' per month Year 2 3 first six months Lyli 1-6) first six months 142: 1-6) first six months tys. 1-6) 18 Months Total Time (in months) Account I has earned earned interest at rate of 's' per month year 1 2 last six months ly; 7-12) tast six months (Y2 : 7-12) Last six months I Ý : 7-12) 18 months 3 Total 18 Value of Account Lofter 3 years P (1+x) (1+s)

has earned interest at 10 Time (in months) rate of Account 2. per month year Q 3 Total Months: 1,3,5,7,9, L (six months) months :13., 5.2LIL_(six months) Morthis:1,3,5, 1, L. {six months) 18 months has earned interest at Time (in months) / Account 2 rate of 's' per month Year 2 2 months: 2,4,6,8, 10, 12 (six months) months: 8,4, 6, 8, 10, 12 (six months) months 2, 4, 6, 8, 10, 12 {six months) 18 months 3 Total Value of Account 2 3 . P (1+)'(1ts)! Value of Account 2 = P(1+2) (Lesja after years 욕 Value of Account 1 years after Explanation Account ! Snitial deposit of p_is compounded @ 80% per month for is manths and compounded @ St. per month for 18 months Account 2 Here also initial deposit of p_is_compounded @ 8% per month fox. 18 months and compounded este per month foxll months. As both the accounts eaons interest at the rate of & fs. for the same time period (ie 18 months), value of account 1 and account 2 after 3 years must be equal .