Lucky Spin: Godly Programming-Chapter 25: Solving with Style

Question: Supose you won 10,000 pesos and you plan to invest it for 5 years. A cooperative group offers 2% simple interest rate per year. A bank offers 2% compounded annually. Which will you choose and why?

Jeff stood in the center while Ms. Lovella stood beside the board, watching his actions.

The room was quiet, except for the soft hum of the fan.

He scratched his head and mumbled, "Alright, I need to compare both, so I’ll start with the simple one."

He then grabbed a piece of chalk and began answering the question.

"Since I already know the formula," he uttered as the sound of writing echoed in the silent classroom.

As he wrote it down:

Formula: I = P × r × t

(Where I is interest, P is principal, r is rate, and t is time in years)

Then, just below that, he listed the values:

Principal (P) = 10,000 pesos

Rate (r) = 2% or 0.02

Time (t) = 1 to 5 year

He wrote it down using a table to make it more presentable. Jeff then paused for a moment.

"Simple interest doesn’t change over time. It’s based only on the original amount. So, for each year, I just multiply the same principal by time."

He began solving year by year, writing each step neatly:

Year 1:

I = 10,000 × 0.02 × 1 = 200

Amount = 10,000 + 200 = 10,200

"So in the first year, I only get 200 pesos. Makes sense."

Year 2:

I = 10,000 × 0.02 × 2 = 400

Amount = 10,000 + 400 = 10,400

"Since it’s simple interest, the 2% applies to the same 10,000 every time and not the growing amount."

Year 3:

I = 10,000 × 0.02 × 3 = 600

Amount = 10,000 + 600 = 10,600

Year 4:

I = 10,000 × 0.02 × 4 = 800

Amount = 10,000 + 800 = 10,800

Year 5:

I = 10,000 × 0.02 × 5 = 1,000

Amount = 10,000 + 1,000 = 11,000

As he then underlined and circled the final result:

"Maturity Value = ₱11,000 after 5 years."

Jeff leaned back and looked at the answer on the board, "So, if I go with the cooperative group using simple interest, I’ll only earn 1,000 pesos in five years. I think this is already correct."

He then glanced at the second part of the question, the one that mentioned compound interest.

"Let’s see what the bank can offer with compounding. Might be small at first, but let’s break it down since I have to finish it less the teacher gets angry," he exclaimed in haste.

As Jeff stood in front of the board, he began to solve the compound interest in the second part of the question.

He started by writing the formula:

A = P(1 + r)^t - This is the compound interest formula

’A’ is the amount after a certain number of years, ’P’ is the principal or starting amount, ’r’ is the interest rate in decimal form, and ’t’ is the number of years.

He looked at the class and continued, and seeing their silent expressions made him tremble, since he was not comfortable being in the spotlight.

He shook his head and refocused himself.

"In this case, the principal P is ₱10,000, the interest rate r is 2 percent or 0.02, and I’m solving it for five years. But instead of calculating it all at once, I’m going to do it year by year so we can see how the interest grows over time."

Year 1: A = 10,000 × (1 + 0.02)

= 10,000 × 1.02 = 10,200

"In the first year, the money grows by 2%. So 2% of 10,000 is 200. Add that to the original, and we get ₱10,200." he calculated as he wrote it down, from a new table for the compound interest.

Year 2: A = 10,200 × 1.02 = 10,404

"Now instead of calculating 2% of the original 10,000 again, we calculate 2% of the new amount, 10,200. That gives us 204 more pesos. Add that, and we now have ₱10,404."

Year 3: A = 10,404 × 1.02 = 10,612.08

"Next, we take 2% of 10,404. That’s about 208.08. Added together, that makes ₱10,612.08."

Year 4: A = 10,612.08 × 1.02 = 10,824.32

"Now it’s 2% of 10,612.08. Each time, the interest grows a little more because the base amount keeps increasing."

Year 5: A = 10,824.32 × 1.02 = 11,040.81

"And finally, 2% of 10,824.32 is around 216.49. Add that, and after 5 years, we end up with ₱11,040.81."

Jeff turned to the class and then to his teacher, Ms. Lovella, who looked at him with a slightly dumbfounded expression.

He began to wonder if he had made a mistake, just from the look on her face.

He looked back at the board, where the final value was underlined and circled:

"Final Answer: ₱11,040.81 after 5 years with compound interest."

"Teacher, I’m done," he said as he put the chalk down on the teacher’s table, waiting for her instruction.

Ms. Lovella, having been called out, snapped out of her dreamy state. She walked over to the blackboard and checked the solution, seeing that everything was correct.

She stared at the table comparing the simple and compound interest, utterly dumbfounded.

Looking at his student, Jeff, who was still standing there waiting for her response, she finally asked,

"How did you solve the problem in simple interest, especially the compound interest?" Ms. Lovella asked.

Jeff scratched the back of his head, confused why she even had to ask.

"Uhm... I just followed the formulas, Ma’am. For simple interest, it’s just P × r × t a very straightforward one since the interest doesn’t change. But for compound, I calculated it year by year, applying the 2% to the new amount each time. It just keeps growing like, interest on top of interest."

Ms. Lovella blinked, still trying to process what she saw on the board.

She glanced at Jeff again, her voice a bit more curious this time.

"And Jeff, how did you get those decimal values from the 2%? I noticed you used 0.02 in your solution. That’s correct, but how were you able to convert it so quickly, without using a calculator or even writing it out on the board first?"

Jeff replied casually, slipping his hands into his pockets since this made him comfortable when a lot of people stared at him.

"Ah, it’s just a shortcut I made, Teacher. I call it ’Shift and Slice’ I just mentally shift the decimal point and slice the percentage."

He looked around at the confused faces of his teacher and classmates.

"Like for 2%, I just move the decimal two places to the left. So 2 becomes 0.02 done. So no calculator was needed. Same trick works for 5%, 12%, even 0.75%. Once you see the pattern, you don’t really need to write it down."

"As for dividing or multiplying decimals? I just break them into whole numbers first, solve it in chunks, then adjust the decimal back at the end. It’s like simplifying before solving, since it’s faster and less messy."

The class went silent. Even Ms. Lovella stared at him for a moment, as if she wasn’t sure if he was still her student or rather her future replacement.

"So, can you explain to the whole class how you solved the question?" Ms. Lovella instructed.

Jeff could not help but heed her words.