Question

Arithmetic Sequence
A man puts $300 into a savings account at the end of each year for 15 yrs. If his money draws 3% simple interest, how much will he have in the account at the end of 15 yrs?

Answer 1

Lets break it down :
At the end of 1st year: 3% interest out of $0 = $0
total = 0+300 = $300
At the end of 2nd year: 3% interest out of $300 = $9
total = 9+300+300 = $609
At the end of 3rd year: 3% interest out of $609 = $18.27
total = 18.27+609+300 = $927.27

So the general term would be:
u(n)=3%*u(n-1)+u(n-1)+300=(0.03+1)*u(n-1)+300
u(n) = 1.03*u(n-1) + 300

Answer 2

@math&ing001 is the answer 426? just making sure

Answer 3

I'm sorry, but it couldn't be $426 because at the end of the 3rd year he already has $927.27 and it's only going to increase. It's gonna be much more at the 15th year.

Answer 4

First thing we could do is make u(n) only dependent of 'n' so we can find u(15) directly.
You can use v(n) = 1.03^n * 300 as geometric sequence
And find its sum, meaning
u(15) = v(1) + v(2) + ... + v(15)
Did you study the sum of a geometric sequence ?

Answer 5

hmm no. But the problem stated that I should use the arithmetic sequence