You borrowed $5,000 from your parents to purchase a used car. You have agreed to make payments of $250 per month plus an additional 1% interest on the unpaid balance of the loan

a. Is this problem an example of a geometric series or an arithmetic series? Support your answer mathematically
b. Find the first year’s monthly payments that you will make and the unpaid balance after each month
c. Find the total amount of interest paid over the term of the loan

Question

You borrowed $5,000 from your parents to purchase a used car. You have agreed to make payments of $250 per month plus an additional 1% interest on the unpaid balance of the loan

a. Is this problem an example of a geometric series or an arithmetic series? Support your answer mathematically
b. Find the first year’s monthly payments that you will make and the unpaid balance after each month
c. Find the total amount of interest paid over the term of the loan

amistre64 · Answer

is the loan got any kind of interest attached to it?
$$B_n=B_n-(P+.1~B_{n-1})$$

amistre64 · Answer

lost a -1 :)

$$B_n=B_{n-1}-(P+.1~B_{n-1})$$
$$B_n=B_{n-1}-.1~B_{n-1}-P$$
$$B_n=B_{n-1}(.9)-P$$
is the recurrsion without any sort of extra interest caclculated on the loan

amistre64 · Answer

its an odd read, but they seem to be suggesting in the questions that interest is owed.

maybe its a 1% interest compounded ...

amistre64 · Answer

in which case the recurrsion is

$$B_n=B_{n-1}(1.01)-P$$which is still not geometric

amistre64 · Answer

as is this works up to an explicit balance equation of:$$B_n=B_o(1.01)^m-P\frac{1-(1.01)^m}{1-(1.01)}$$

amistre64 · Answer

lol, i thougth of using m for month,  but have n left on the left ... minor details tho

amistre64 · Answer

somethings still off, i cant get a good read on the question to be sure