请问PV为什么这样计算？请解释

NO.PZ2018062016000014问题如下Tom htwin ughters LuanLily 12 years ol Six years later, both will stu in a famous university in California for four years with a tuition fee of $6,000 paithe beginning of eayeper person. Assume the annuscount rate is 5%, toy Tom shoulprepare:A.$16,670B.$33,340C.$31,753B is correct. Six years later, Tom will ptuition fee of $12,000 eayeanlast for 4 years, he htwo ughters. The payment is paiin the front, therefore set the calculator BGN mo aninput: N=4, I/Y=5%, PMT=12,000, FV=0, then PV=44678.98. The value of tuition funye6 is $44,678.98, so the present value is $44,678.98/(1+5%)6=$33,340.为什么前六年不用利率除以6加一‘而是直接加上百分之五什么情况下用EAR、 什么时候括号外是每年次数乘以年数 、什么时候不用除以次数直接相加利滚利

NO.PZ2018062016000014问题如下Tom htwin ughters LuanLily 12 years ol Six years later, both will stu in a famous university in California for four years with a tuition fee of $6,000 paithe beginning of eayeper person. Assume the annuscount rate is 5%, toy Tom shoulprepare:A.$16,670B.$33,340C.$31,753B is correct. Six years later, Tom will ptuition fee of $12,000 eayeanlast for 4 years, he htwo ughters. The payment is paiin the front, therefore set the calculator BGN mo aninput: N=4, I/Y=5%, PMT=12,000, FV=0, then PV=44678.98. The value of tuition funye6 is $44,678.98, so the present value is $44,678.98/(1+5%)6=$33,340.6年后为什么不是19那个点开始第一笔现金流到22节点呢？这种题目一直分不清这中间的节点和具体N是怎么算出来的，一次都没做对过，有没有容易理解的方法

NO.PZ2018062016000014 问题如下 Tom htwin ughters LuanLily 12 years ol Six years later, both will stu in a famous university in California for four years with a tuition fee of $6,000 paithe beginning of eayeper person. Assume the annuscount rate is 5%, toy Tom shoulprepare: A.$16,670 B.$33,340 C.$31,753 B is correct. Six years later, Tom will ptuition fee of $12,000 eayeanlast for 4 years, he htwo ughters. The payment is paiin the front, therefore set the calculator BGN mo aninput: N=4, I/Y=5%, PMT=12,000, FV=0, then PV=44678.98. The value of tuition funye6 is $44,678.98, so the present value is $44,678.98/(1+5%)6=$33,340. 按照答案写的计算顺序，第一步计算N=4, I/Y=5%, PMT=12,000, FV=0, then PV是44678.98，这里为什么用先付年金的公式呢，交学费的类似题目，比如讲义P17页的例题中第一步计算器也是用后付年金的公式，按照例题思路第二步用计算器n应该是5啊，为啥是6

NO.PZ2018062016000014问题如下Tom htwin ughters LuanLily 12 years ol Six years later, both will stu in a famous university in California for four years with a tuition fee of $6,000 paithe beginning of eayeper person. Assume the annuscount rate is 5%, toy Tom shoulprepare:A.$16,670B.$33,340C.$31,753B is correct. Six years later, Tom will ptuition fee of $12,000 eayeanlast for 4 years, he htwo ughters. The payment is paiin the front, therefore set the calculator BGN mo aninput: N=4, I/Y=5%, PMT=12,000, FV=0, then PV=44678.98. The value of tuition funye6 is $44,678.98, so the present value is $44,678.98/(1+5%)6=$33,340.一个孩子如果第六年初（第五年末）交6000，那后付计算器算出来的PV不是第四年末的PV21275.7吗？为什么是第五年末呢？

NO.PZ2018062016000014 问题如下 Tom htwin ughters LuanLily 12 years ol Six years later, both will stu in a famous university in California for four years with a tuition fee of $6,000 paithe beginning of eayeper person. Assume the annuscount rate is 5%, toy Tom shoulprepare: A.$16,670 B.$33,340 C.$31,753 B is correct. Six years later, Tom will ptuition fee of $12,000 eayeanlast for 4 years, he htwo ughters. The payment is paiin the front, therefore set the calculator BGN mo aninput: N=4, I/Y=5%, PMT=12,000, FV=0, then PV=44678.98. The value of tuition funye6 is $44,678.98, so the present value is $44,678.98/(1+5%)6=$33,340. 6年后的年初需要交资金，那么在时间轴上体现为17岁末18岁初？ 折算到12岁（toy）是指12岁初还是末呢 这个题意现金流怎么把控，（此外延伸问一下其他CFA考试中涉及的现金流末尾一般是）