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Math Questions

Equation of value



Question ((1))

a delbt of $3000 due six yrs from now is instead to be paid off by three payments: $500 now, $1500 in three yrs, and a final payment at the end of five yrs. What would this payment be if an interest rate of 6 % compounded annually is assumed?

Answer

500(1.06)^5 + 1500(1.06)^2 + x = 3000(1.06)^-1

x = 3000(1.06)^-1 - 500(1.06)^5 - 1500(1.06)^2

x = $475.68



Question ((2))


A bebt of $600 due in three yrs and $800 due in four yrs is to be repaid by a single payment two yrs from now. If the interest rate is 8 % compounded semiannually, how much is the payment?


Answer





x = 600(1.04)^-2 + 800(1.04)^-4

x = $1238.58


Any body can explain Question((2)) to me?

Thank you

第2年放x元, 計複息到第3年時取走600, 餘額計複息到第4年時剛好等於800
即[x(1.04)^2-600](1.04)^2=800
拆開就是x = 600(1.04)^-2 + 800(1.04)^-4