compound interest

There are 2 steps, first we need to find the present value of the sum if we deposit 1000 every month for 20 years. Then we calculate the total that we can get in 20 years time.

(i) as interest is calculated half yearly, present value of the sum =

6000 *(1-(1+0.02)^-40)/0.02
=164132.86

the sum in 20 years = 164132.86*(1.02)^40=362411.89


(ii) as interest is calculated monthly, PV of the sum =

1000*(1-(1+0.01)^-240)/0.01
=165021.86

the sum in 20 years = 165021.86*(1.01)^240=366774.63

Qii) is still OK for calculation, but for Qi) we need to make some assumptions before we start the calculation:
1) 2nd month of deposit $1000 cannot be added into the 1st month deposit, as the period is counted as half-year. Therefore, it should be calculated separately.
2) for the last 6 months of 20 years, there is no interest rate given by the bank, as the deposit period is 6 months.
Based on the above assumptions, then we can start the calculation. I used Excel to generate a repeat formula for easy calculation.
Pls refer to: http://i404.photobucket.com/albums/pp124/mr_gary_cheung/calculation.jpg
If you want to know the repeated formula, I can send the EXCEL sheet for your study.
ANSWERS:
Qi) Interest calculated half-yearly: $362,411.8991
Qii) Interest calculated monthly: $367,997.2082

2009-01-21 18:01:57 補充：
To myisland8132:

well, the question is asking... Please provide formula if possible... doesn't mean I have to provide the formula wor.

2009-01-21 18:02:06 補充：
I try to figure out the formula to calculate the answers directly, but it is so complicated. It is easier to use EXCEL for repeat calculation. So, i use EXCEL to find out the answers.

By the way, what do you think about my answers? correct or not?

你的問題不易答﹐除非你找到個操soa exam 2 操到巔峰狀態的人才可以有信心一定答對。若你有答案我可以對番本書做﹐0甘就應該可以做到。

2009-01-21 17:43:45 補充：
上面個位大大會錯意﹐Please provide the formula if possible bor