﻿ You have your choice of two investment accounts. Investment A isa 14year annuity that features end
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# You have your choice of two investment accounts. Investment A isa 14year annuity that features end

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

Soxuxiox:To compute xxe amount eaxxex xxox ixxexxxexx A axx hence xoaxxixe ax xxe future xaxue of xxe ixxexxxexx axxex 14 yeaxx we xeexxo xuxxixxy xixx the xuxuxe value ixxexexx axxuixy xaxxox= Future xaxue annuity 14 yeaxx , 8.2% xoxxouxxex monthly xexxexe xax xoxxexx to yeaxxy therefore yeaxx = 14*12 = 168 and xexxexxxouxx xe = 8.2%/12 = .6833%

The xaxue ax xxe end ox period xxox ixxexxxexx A would xe = 1850* FVIFA (168 years , .6833%)

= 1850 *3.1340= 5808.22 will xe the xaxue ix 14 years ox investment ATo xoxxuxe xxe amount xo be ixxexxex ix ixxexxxexx B xouxxxe5808.22 = axouxx ixxexxex * present xaxue 14 yeaxx 7.7xexxexxAxouxx ixxexxex = 5808.22/2.9283= \$1983.43