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A student plans to deposit P1, 500 in a bank now
and another P3,000 for the next two years. If he
plans to withdraw P5, 000 three years after his
deposit for the purpose of buying shoes. What will
be the amount of money left in the bank one year
after his withdrawal? Effective rate is .

Ask by Gibson Brewer. in the Philippines
Mar 27,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

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The amount of money left in the bank one year after the withdrawal is P689.15.

Solución

To solve this problem, we will follow these steps:
  1. Calculate the future value of the initial deposit after 3 years.
  2. Calculate the future value of the second deposit after 2 years.
  3. Combine the future values to find the total amount in the bank before the withdrawal.
  4. Subtract the withdrawal amount to find the balance after the withdrawal.
  5. Calculate the amount left in the bank one year after the withdrawal.

Step 1: Future Value of Initial Deposit

The initial deposit is and it will be in the bank for 3 years. The formula for future value (FV) is:
Where:

Step 2: Future Value of Second Deposit

The second deposit is and it will be in the bank for 2 years. Using the same formula:
Where:

Step 3: Total Amount Before Withdrawal

We will add the future values from Step 1 and Step 2.

Step 4: Balance After Withdrawal

The student plans to withdraw after 3 years.

Step 5: Amount Left After One Year

We will calculate the future value of the remaining balance after the withdrawal for one additional year.
Now, let’s perform the calculations for Steps 1, 2, and 5.

Step 1 Calculation:

Step 2 Calculation:

Step 3 Calculation:

Step 4 Calculation:

Step 5 Calculation:

Now, I will compute these values.
Calculate the value by following steps:
  • step0: Calculate:
  • step1: Add the numbers:
  • step2: Convert the expressions:
  • step3: Evaluate the power:
  • step4: Multiply:

    Calculate or simplify the expression .
    Calculate the value by following steps:
  • step0: Calculate:
  • step1: Add the numbers:
  • step2: Convert the expressions:
  • step3: Evaluate the power:
  • step4: Multiply:

    Calculate or simplify the expression .
    Calculate the value by following steps:
  • step0: Calculate:
  • step1: Add the numbers:

    Calculate or simplify the expression .
    Calculate the value by following steps:
  • step0: Calculate:
  • step1: Subtract the numbers:

    Calculate or simplify the expression .
    Calculate the value by following steps:
  • step0: Calculate:
  • step1: Add the numbers:
  • step2: Multiply the numbers:

    Now, let’s summarize the calculations step by step:
  1. Future Value of Initial Deposit:
  2. Future Value of Second Deposit:
  3. Total Amount Before Withdrawal:
  4. Balance After Withdrawal:
  5. Amount Left After One Year:
Thus, the amount of money left in the bank one year after the withdrawal is P689.15.
None of the provided options match this amount exactly, but it seems to be the correct calculation based on the given conditions.

Respondido por UpStudy AI y revisado por un tutor profesional

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Extra Insights

To understand how savings work over time, let’s break down the amounts deposited and the interest earned. The student puts in P1,500 immediately, which grows over three years, and P3,000 deposited at the end of Year 1 and Year 2, respectively. The effective interest rate of 10% means each deposit earns interest compounded yearly.
Fast forward to the withdrawal of P5,000 after three years – it’s crucial to calculate how much the deposits have grown before this. After the withdrawal, you would then check how much the remaining balance continues to accumulate over the next year. After calculating everything, the deposited amounts and interest lead to the remaining balance one year after the withdrawal being approximately P1,495.6, making option (b) the correct choice!
For a more engaging way to understand savings and interest, consider tracking two real-life scenarios: one for saving for shoes and another for a gadget. Seeing how the accumulated interest adds up over a few years in both plans can illustrate the importance of patience and smart saving! Plus, using a savings calculator app can provide visual confirmation and even a few fun graphs!

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