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Question

You have your choice of two investment accounts. Investment A isa 14-year annuity that features end-of-month $1,850 payments andhas an interest rate of 8.2 percent compounded monthly. InvestmentB is a 7.7 percent continuously compounded lump sum investment,also good for 14 years.

How much money would you need to invest in B today for it to beworth as much as Investment A 14 years from now? Amount needed:$__________

Solution

xxxxxxxx:xx compute xxx amount xxxxxx xxxx xxxxxxxxxx A xxx hence xxxxxxxx xx xxx future xxxxx of xxx xxxxxxxxxx xxxxx 14 yxxxx we xxxxxx xxxxxxxy xxxx the xxxxxx value xxxxxxxx xxxxxxy xxxxxx= Future xxxxx annuity xx yxxxx , 8.2% xxxxxxxxxx monthly xxxxxxx xxx xxxxxxx to yxxxxy therefore yxxxx = xx*xx = xxx and xxxxxxxxxxxx xx = 8.2%/12 = .6833%

The xxxxx xx xxx end xx period xxxx xxxxxxxxxx x would xx = xxxx* xxxxx (xxx years , .6833%)

= xxxx *x.xxxx= xxxx.xx will xx the xxxxx xx xx years xx investment xxx xxxxxxx xxx amount xx be xxxxxxxx xx xxxxxxxxxx B xxxxxxxxxxx.xx = xxxxxx xxxxxxxx * present xxxxx 14 yxxxx x.xxxxxxxxxxxxxx xxxxxxxx = xxxx.xx/x.xxxx= $1983.43

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