Definition §

Compound Interest w/ Sequences

Unlike simple interest, Compound Interest can be expressed as a Geometric Sequence, and increases Exponetially.

Recursive §

Where: = Investment Rate increased by 1, e.g. 5% = 1.05 instead of 0.05 = Amount Added every Term, e.g. $200 added at the end of every Term after Interest is applied.

Recursive (For finding r) §

Where: = Ratio = Time Period, e.g. 4 for quarters, 12 for months, 26 for fortnight, 1 for years, all these are for when is defined per annum, (p.a.) e.g:

Explicit (Not sure if right) §

Finding Interest over a life-time §

Where: = Term where investment ends = Principal = Amount taken / putting in each term (e.g. +200 for added 20 each term for 10 terms, or -200 for removed 20 each term for 20 terms.)

Examples §

Question

Shaun plans to travel overseas in June 2020 so he decides to save for his trip by making** monthly deposits of 250** with all future deposits being made on the first day of the month.

How much will be in his account on the 31st May 2020.

---

Divided by twelve so that the interest is respective to every month, therefore each term in the following sequence is equal to one month.

Alternative Formulas

[!multi-column]

Starting at 1 |

1 | July 2017
2 | August 2017
3 | September 2017
4 | October 2017
5 | November 2017
6 | December 2017
7 | January 2018
8 | February 2018
9 | March 2018
10 | April 2018
11 | May 2018
12 | June 2018
13 | July 2018

[…]

34 | April 2020 - 9559.20 35 | May 2020 - 9876.1 36 | June 2020 - 10195.25 37 | July 2020 - 10516.62

Zero-indexed |

0 | July 2017
1 | August 2017
2 | September 2017
3 | October 2017
4 | November 2017
5 | December 2017
6 | January 2018
7 | February 2018
8 | March 2018
9 | April 2018
10 | May 2018
11 | June 2018
12 | July 2018

[…]

33 | April 2020 - 9559.20 34 | May 2020 - 9876.1 35 | June 2020 - 10195.25 36 | July 2020 - 10516.62

Therefore, to get the answer, you have to find , since it represents June, which is 35 months after July 2017, The date we need to find is the 31st May 2020, which is essentially June but without $250 added. Therefore:

10915.25 - 250 = 9945.25

"Question"

36% p.a, Compounded monthly 65 Repayments

,

Question

200 added at the end of each month after interest.

, OR ,

Question where explicit Compound Interest is applied wrong.