discountrate於两个投资计画Thereare2differentinvestmentplans:A:$10,000annualperpetuityB:10year,$22,000annualpayments(annuity)bothplanswillmaketheirfirstpaymentoneyearfromtoday.Whatdiscountratewillmakethe2plansin

Question

discount rate 於两个投资计画
There are 2 different investment plans:
A:$10,000 annual perpetuity
B:10 year,$22,000 annual payments (annuity)
both plans will make their first payment one year from today.What discount rate will make the 2 plans indifferent?
请帮忙计算,要breakdown 如何计.Thanks a million!

Answer 1

我来回答：
根据无穷等比递降数列求和公式,第一个投资的现值为：10000/（1-x）,x在这里就是折现率discount rate,
根据有限等比数列求和公式,第二个投资的现值是：22000（1-x的十次方）/（1-x）,
要两者现值相等的折现率根据方程10000/（1-x）=22000（1-x的十次方）/（1-x）,
经简化,方程演变为最简形式：x的10次方=6/11,你用计算器就可以开x的十次方.
这题不简单,请给分哦,亲.