Question 32737
the equation for compounded is:
y=a(1 + r/n)^(tn)
y is final amount
a is initial amount
r is rate
n is compounded per times per year
t is time in years
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A person has the option of satisfying a debt by either paying $5000 now and $5000 in 2 years; rate is 8% compounded quarterly?
the result: 5000 (now) + final amount (y) .... so:
y=a(1 + r/n)^(tn)
y=5000(1 + .08/(1/4))^((1/4)*2)
y=5000(1.32)^(1/2)
y=5744.56
the result: 5000 + 5744.56 = $10,744.56
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or by paying $3000 now, $3000 a year from now, and a final payment of x dollars in 2 years from now. Determine the amount of final payment if the interest rate is 8% compounded quarterly?
the result: 3000 + final amount + final amount
y=a(1 + r/n)^(tn)
y=3000(1+.08/(1/4))^(1/4)
y=3000(1.32)^(1/4)
y=3215.62
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y=a(1 + r/n)^(tn)
y=3000(1.32)^(1/2)
y=3446.74
the result: 3000 + 3215.62 + 3446.74 = $9,662.36
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If I was the person, I would choose the $3,000 deal!