2u Mathematics Marathon v2.0 (1 Viewer)

[pLuvia]

Time to start this again, point of this thread is to test each other's maths skills, general revision etc.

General rule: A person posts up a question (not homework-help questions) and then another person answers it in spoilers and after they answer they put up another question for the next person to answer

How to do spoilers : [spoiler ]Like this[/spoiler ], but without the spaces in between the brackets so without it, it would be something like this

Spoiler

Like this

I'll start off to get the ball rolling, last question from the previous marathon

Question

Stephen has a loan of 100,000.00 to pay. each month, interest of 0.8% is charged on the outstanding amount
a) If stephen pays 5,000 each month starting one month from now how long will it take him to repay the loan?
b) Now suppose stephen pays different amounts every months, but according to the rule that for every dollar of the balance, he'll pay eight cents, so he'll pay more initially, but less later. Find the outstanding amount after the n-th payment

 

[-pari-]

have only done part A so person after me can do part B instead of me putting up a new question....

didn't do part B coz wasn't sure if my first bit was right...could some one plz check?

Spoiler

A1 = 5000 - M (no interest on first amount - he pays at the beginning of the month)
A2 = (A1)x 1.08 - M
= 5000 x 1.08 - M(1.08 - 1)

A3 = 5000 x 1.08^ 2 - M (1.08^ 2 - 1.08 - 1)

Sn = [1.08 (1.08^n -1) ]/1.08 - 1

80 000 = [1.08 (1.08^n - 1) ]
74075.07 = 1.08^n
n = around 145.69
add one for the first month without interest 146.69 months