Question 4 20 pts You need $60,000 in today\'s buying power, 5 years from now. Y

Question

Question 4 20 pts You need $60,000 in today's buying power, 5 years from now. You can earn 2% APR in real terms on your investments. How much must you invest (a different amount each year), starting next year for 4 years to just meet your needs, if you expect inflation to be 4% per year? The amount you invest should just maintain the real cash values. Year 1 Year 2 Year 3 Year 4 $14,101 $14,665 $15,251 $15,861 O Year 1 Year 2 Year 3 Year 4 $15,882 $16,517 $17,178 $17,865 O Year 1e Year 3 Year 4 $15,585 $16,208 $16,857 $17,531 Year 1 Year 2 Year 3 Year 4 $14,843 $15,437 16,054 $16,696

Explanation / Answer

We need in 5 years the todays buying power of 60000 that is we need 60000 in real terms 5 years from now

Let real amount be x per year

Future value in year 5 of amounts saved till year 1-4=x*1.02^4+x*1.02^3+x*1.02^2+x*1.02

Hence,

x*1.02^4+x*1.02^3+x*1.02^2+x*1.02=60000

=>x=60000/(1.02^4+1.02^3+1.02^2+1.02)
=>x=14271.98545

Nominal amounts will be:real amount*(1+inflation)^time
Year1:=14271.98545*1.04=14843
Year2:=14271.98545*1.04^2=15437
Year3:=14271.98545*1.04^3=16054
Year4:=14271.98545*1.04^4=16696

Option D

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