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# help

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Luke is borrowing \$10,000 from the bank. The bank offers him a choice between two 10-year payment plans:

Plan 1. Luke's debt accumulates 10% annual interest which compounds quarterly. Luke pays off half his balance after 5 years, and the rest at the end of the 10 years.

Plan 2. Luke's debt accumulates 10% annual interest which compounds annually. Luke pays off his full balance at the end of the 10 years.

What is the (positive) difference between Luke's total payments under Plan 1 and his total payments under Plan 2? Round to the nearest dollar.

Jan 16, 2019
edited by Guest  Jan 16, 2019

#1
+28025
0

Plan1    Luke essentially borrows two 5000 loans....one he pays back in 5 years and the other accumulates interest for 10 years before he pays it back.

5000 (1.025)^20 = 8193.08   is Luke's first payment...this is also the value of his second 5000 loan at this time.........

8193.08 (1.025)^20 = 13425.32    = Luke's second payment to pay off his entire balalnce

Total payments  8193.08 + 13425.32 = \$ 21618.40

Plan 2 Luke borrows 10000 and pays off entirely at end of 10 years

10000(1.1)^10 = \$ 25937.42

Plan 2 will cost him    25937.42 - 21618.4 =~~ \$ 4319.00 more than plan 1 (rounded)

(THANX gues for noticing my error on interest in plan2 !)

Jan 16, 2019
edited by ElectricPavlov  Jan 16, 2019
edited by ElectricPavlov  Jan 16, 2019
edited by ElectricPavlov  Jan 16, 2019

#1
+28025
0

Plan1    Luke essentially borrows two 5000 loans....one he pays back in 5 years and the other accumulates interest for 10 years before he pays it back.

5000 (1.025)^20 = 8193.08   is Luke's first payment...this is also the value of his second 5000 loan at this time.........

8193.08 (1.025)^20 = 13425.32    = Luke's second payment to pay off his entire balalnce

Total payments  8193.08 + 13425.32 = \$ 21618.40

Plan 2 Luke borrows 10000 and pays off entirely at end of 10 years

10000(1.1)^10 = \$ 25937.42

Plan 2 will cost him    25937.42 - 21618.4 =~~ \$ 4319.00 more than plan 1 (rounded)

(THANX gues for noticing my error on interest in plan2 !)

ElectricPavlov Jan 16, 2019
edited by ElectricPavlov  Jan 16, 2019
edited by ElectricPavlov  Jan 16, 2019
edited by ElectricPavlov  Jan 16, 2019
#2
+1

EP: Good Job!. A slight oversight. Plan 2 "accumulates 10% annual interest which compounds annually."

\$10,000 x {1.10}^10 = \$25,937.42.

Jan 16, 2019
#3
+28025
0

Yep, thanx !...I overlooked that....will edit....

ElectricPavlov  Jan 16, 2019