An individual deposits Php 100,000 into an account that compounds annually at 12%. However, starting
from the 2nd year, the individual withdraws Php 15,000 at the beginning of each year. After how many
years will the account balance fall below Php 10,000? (Assume withdrawals are made before interest for
the year is applied.)

To solve this problem, we need to model the behavior of the account balance over time. The process follows these steps:

1. **Initial Deposit**: Php 100,000 is deposited in the account.
2. **Withdrawals**: Php 15,000 is withdrawn at the beginning of each year starting from the 2nd year.
3. **Annual Interest**: The account earns 12% interest annually, which is applied after the withdrawal is made.

We will compute the balance at the start of each year and apply the 12% interest after subtracting the Php 15,000 withdrawal, until the balance falls below Php 10,000.

Let \( B_n \) represent the balance at the start of the \( n \)-th year (before the withdrawal), and the balance evolves as follows:

\[
B_1 = 100,000 \quad \text{(initial deposit)}
\]

For \( n \geq 2 \):

\[
B_n = (B_{n-1} - 15,000) \times 1.12
\]

The goal is to find the smallest \( n \) such that \( B_n < 10,000 \).

Let's compute this step by step. I'll calculate the balance year by year.After 12 years, the account balance falls below Php 10,000. Specifically, in the 13th year, the balance drops to Php 858, which is well below the threshold.

Would you like more details or have any questions?

Here are 5 related questions you might find useful:

1. What is the balance at the end of each of the first 5 years?
2. How would the timeline change if the interest rate were 10% instead of 12%?
3. How much total interest is earned over the entire period before the balance falls below Php 10,000?
4. How would the account evolve if the withdrawal amount were Php 20,000 instead of Php 15,000?
5. What if the interest compounds quarterly instead of annually?

**Tip**: Always track both withdrawals and interest compounding carefully to manage investment growth.

An individual deposits Php 100,000 into an account that compounds annually at 12%. However, starting from the 2nd year, the individual withdraws Php 15,000 at the beginning of each year. After how many years will the account balance fall below Php 10,000? (Assume withdrawals are made before interest for the year is applied.)

Solve a real-world compound interest problem where an individual deposits Php 100,000 into an account with 12% annual interest, but withdraws Php 15,000 each year. Learn how to calculate the year the balance falls below Php 10,000. Suitable for advanced high school or college students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation