1)Find the amount if $2000 is invested at 5% compounded continuously for 4 years

Question

1)Find the amount if $2000 is invested at 5% compounded continuously for 4 years. 2)Find the principal needed now to get $600 in 3 months at 5% compounded continuously. 3)If $1000 is invested at 3% compounded continuously, what is the amount after 5 years? How much interest is earned? Amount after 5 years = $ Interest earned = $

Explanation / Answer

The equation for continuous compounded interest is --- F = Pe^(rt) where F is the future value , P is the principle , r is the interest rate as a decimal , and t is the time in years . For part 1) , we have P = 2000 , r=.05 , and t= 4years . We want F : -------------------------------------------------------------------------------- F = 2000e^(.05(4)) = 2,442.81 dollars ------- solution 1 . ------------------------------------------------------------------------------------- For part 2) , we have F =600 , r = .05 , and t = 3/12 = .25years . We want P: 600 = Pe((.05)(.25)) ----> now solve for P ----> --------------------------------------------------------------------------------- P=600/[e^((.05)(.25))] = 592.55 dollars -------- solution 2 . ------------------------------------------------------------------------------------- For part 3 ) , we have P = 1000 , r = .03 , and t = 5 years . They first want the future value : ------------------------------------------------------------------------- F = 1000e^((.03)(5)) = 1,161.83 dollars ---- solution 3 . The interest is : --------------------------------------------------------------------------------- ----------------------------------------------------------------------------------- I = F - P = 1,161.83 - 1000 = 161.83 dollars --- solution 4 . -----------------------------------------------------------------------------------

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