大侠再接再厉Lizais30now,earningaconstantlaborincomeof$50,000perannum.Sheisexpectedtoretireat60,andthenlivefor20moreyearsafterherretirement.Supposethatallcashflowsareoccurredattheendofeachperiod,anddeposi

Question

大侠 再接再厉
Liza is 30 now,earning a constant labor income of $50,000 per annum.She is expected to retire at 60,and then live for 20 more years after her retirement.Suppose that all cash flows are occurred at the end of each period,and deposit rate is 5% per annum,compounded annually.Suppose that Liza has participated in the social security system by paying a 10% tax on salary every year,in order to have a pension of $12,000 every year from the retirement till the end of her life.What rate is offered by the Social Security System?

Answer 1

假设Social Security System的利息为r
每年存入SSS为：50,000*10% = 5,000
存60-30 = 30年
则复利30年用r折现,现值为M
M = 5000/r * (1- 1/(1+r)^30)
另一方面,退休后,每年SSS返还12,000
一共返还20年
则在复利计算折现20年,然后再折现到现在,使其现值等于M.
M = [12000/r * (1- 1/(1+r)^20) ] / (1+r)^30
联立两式,求得r = 1.8688%
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