Robin borrows $11400 which will be paid back in equal monthly installments, each of which includes a 0.8 % interest charge on the unpaid balance.
Suppose that Robin pays $470 on his loan each month. His first payment includes $91.2 (that is, 0.008 x 11400) in interest. The remaining $378.8 reduces his debt,
leaving $11021.2 owed. Continue this pattern, making a sequence of the amount Robin still owes after he makes his payment at the end of each of the first six months.
First Month $11021.2
Second Month
Third Month $
Fourth Month $
Fifth Month S
Sixth Month $
After how many months will Robin make his final payment?
How much will his final payment be? $
(Remember that his final monthly payment will be what he owed the previous month plus interest.)
of this problem round all answers to the nearest cent

Robin borrows $11,400 which will be paid back in equal monthly instalments of $470, each of which includes a 0.8 % interest charge on the unpaid balance.

To determine the amount Robin still owes at the end of each month, we multiply the amount owed at the beginning of the month by 1.008 and subtract the monthly payment of $470:

[tex]\textsf{First month:}\quad (11400\cdot 1.008)-470=11021.20[/tex]

[tex]\textsf{Second month:}\quad (11021.20\cdot 1.008)-470=10639.3696=10639.37[/tex]

[tex]\textsf{Third month:}\quad (10639.37\cdot 1.008)-470=10254.48496=10254.48[/tex]

[tex]\textsf{Fourth month:}\quad (10254.48\cdot 1.008)-470=9866.51584=9866.52[/tex]

[tex]\textsf{Fifth month:}\quad (9866.52\cdot 1.008)-470=9475.45216=9475.45[/tex]

[tex]\textsf{Sixth month:}\quad (9475.45\cdot 1.008)-470=9081.2536=9081.25[/tex]

So, the iterative formula for the amount still owing at the end of the (n + 1)th month is:

[tex]x_{n+1}=1.008x_n-470[/tex]

If we continue this pattern, the amount Robin still owes at the end of the 27th month will be $34.28. (See attachment).

So, he will make his final payment in the 28th month and it will be the amount still owing ($34.28) plus 0.8% interest:

[tex]34.28 \cdot 1.008=34.55424=34.55[/tex]

Therefore, the final payment will be $34.55.