Question

Discrete math: Someone invests $3,000 at 12% annual interest, compounded quarterly. Let A[sub(n)] represent the amount after n years.

Find recurrence relation for A[sub(0)], A[sub(1)], ...

Answer 1

Have you considered accumulating at 4% per quarter?

Answer 2

so like An (n is sub) = 3000 * (1/4 * 0.12)n? how off am I on that

but anyway wouldn't it be 3%/quarter since it's 12% annually 4 quarters (by def) in a yr so 12/4 = 3%... or am i even completely incapable of simple math...

Answer 3

no it's gotta be n-1? no i don't know how to get a recursive relation itself from that i need an example.

Answer 4

A(0) = 3000 , since we start at 3000

Answer 5

The general formula for compounding interest n times a year is

A(t) = P ( 1 + r/n) ^ (n*t)

Answer 6

but you want a recurrence relation

Answer 7

what's r? why 1 + ?

Answer 8

r is the annual rate of interest , n is the number of times you compound a year

Answer 9

this is a different n than what you are using

Answer 10

oh gotcha..

Answer 11

right yeah

Answer 12

The general formula for compounding interest k times a year is
A(t) = P ( 1 + r/k) ^ (k*t)

Answer 13

:)

Answer 14

ok thank you but what is P?

Answer 15

P is the principal , here 3000

Answer 16

So A(n) = P ( 1 + r/k ) ^(k*n) ) = 3000 (1 + 0.12/0.25) ^(0.25*n)?

Answer 17

sure much appreciated

Answer 18

oh wait, the directions say
Let A[sub(n)] represent the amount after n years.

Answer 19

so you are right, n is equal to t in the formula

Answer 20

lets make a table

Answer 21

yeah ok so then you don't need to take a different approach is what you're saying? lol my understanding is sufficient?

Answer 22

let's