SOLUTION: A person has the option of satisfying a debt by either paying $5000 now and $5000 in 2 years, or by paying $3000 now, $3000 a year from now, and a final payment of x dollars in 2 y

Question 32737This question is from textbook introductory mathematical analysis
: A person has the option of satisfying a debt by either paying $5000 now and $5000 in 2 years, 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?
Thank you! This question is from textbook introductory mathematical analysis

Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
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
---------------------------------------------------------------------------
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
---------------------------------------------------------------------------
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
------------------------
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
-------------------------------------------------------------------------------
If I was the person, I would choose the $3,000 deal!
RELATED QUESTIONS
Hak Young has accumulated some credit card debt while he was in college. His total debt... (answered by Theo,math_tutor2020)

Ahmed wants to pay back his debt to the bank. He has already paid back 60% of the initial (answered by jim_thompson5910)

Steve, a recent tetiree, requires $5000 per year in extra income. He has $70,000 to... (answered by 466158)

Betsy a retiree, requires $5000 per year in extra income.she has $60000 to invest and can (answered by Earlsdon)

Betsy, a recent retiree, requires $5000 per year in extra income. She has $50000 to... (answered by Boreal)

A $5,000 debt on a credit card will take 32 years to repay if only the minimum monthly... (answered by KMST)

Hak Young is daunted by that monthly payment amount and is trying to figure out how he... (answered by greenestamps)

a principal of $5000 is invested in an account paying an annual rate of 5%. find the... (answered by DrBeeee)

Hak Young has accumulated some credit card debt while he was in college. His total debt... (answered by math_tutor2020)