F.6 math geometric sequence~2
2011-10-04 4:03 am
Miss Ng joins a savings plan, and deposits $2000 in a bank at the beginning of each month at an interest rate of 4% p.a. compounded monthly for 3/2 years. (a) (i) How much has Miss Ng deposited in the bank after 3/2 years? (ans. $36000) (ii) Find the balance on Miss Ng’s account in the bank after 3/2 years. (ans. $37162)(b) If Mr. Chan wants to obtain $100000 after 3/2 years, how much should be deposit each month? (ans. $5382)*Please list the detailed steps
回答 (1)
2011-10-04 4:32 am
✔ 最佳答案
(a)(i) 2000 * 18 = 36000 (a)(ii) 2000[ (1 + 4%/12)^18 + (1 + 4%/12)^17 ... + (1 + 4%/12)]
= 2000(1.003 + ... + 1.003^18)
= 2000(1.003)(1.003^18 - 1)/(0.003)
= 37162
(b) Let the required dollar is P
P(1.003)(1.003^18 - 1)/(0.003) > 100000
P > 5381.8673
So, Mr. Chan should deposit at least 5382
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