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.
+37158 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 !)
+37158 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 !)
