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

Question

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

UpStudy AI · Accepted Answer

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 $$ P1,500 $$ and it will be in the bank for 3 years. The formula for future value (FV) is:

$$
FV = P(1 + r)^n
$$

Where:
- $$ P = 1500 $$
- $$ r = 0.10 $$
- $$ n = 3 $$

### Step 2: Future Value of Second Deposit
The second deposit is $$ P3,000 $$ and it will be in the bank for 2 years. Using the same formula:

$$
FV = P(1 + r)^n
$$

Where:
- $$ P = 3000 $$
- $$ r = 0.10 $$
- $$ n = 2 $$

### 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 $$ P5,000 $$ 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:
$$
FV_1 = 1500(1 + 0.10)^3
$$

#### Step 2 Calculation:
$$
FV_2 = 3000(1 + 0.10)^2
$$

#### Step 3 Calculation:
$$
Total = FV_1 + FV_2
$$

#### Step 4 Calculation:
$$
Balance\_after\_withdrawal = Total - 5000
$$

#### Step 5 Calculation:
$$
Amount\_left = Balance\_after\_withdrawal(1 + 0.10)
$$

Now, I will compute these values.
Calculate the value by following steps:
- step0: Calculate:
  $$1500\left(1+0.1\right)^{3}$$
- step1: Add the numbers:
  $$1500\times 1.1^{3}$$
- step2: Convert the expressions:
  $$1500\left(\frac{11}{10}\right)^{3}$$
- step3: Evaluate the power:
  $$1500\times \frac{1331}{1000}$$
- step4: Multiply:
  $$\frac{3993}{2}$$
Calculate or simplify the expression $$ 3000*(1 + 0.10)^2 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$3000\left(1+0.1\right)^{2}$$
- step1: Add the numbers:
  $$3000\times 1.1^{2}$$
- step2: Convert the expressions:
  $$3000\left(\frac{11}{10}\right)^{2}$$
- step3: Evaluate the power:
  $$3000\times \frac{121}{100}$$
- step4: Multiply:
  $$3630$$
Calculate or simplify the expression $$ 1996.5 + 3630 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$1996.5+3630$$
- step1: Add the numbers:
  $$5626.5$$
Calculate or simplify the expression $$ 5626.5 - 5000 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$5626.5-5000$$
- step1: Subtract the numbers:
  $$626.5$$
Calculate or simplify the expression $$ 626.5*(1 + 0.10) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$626.5\left(1+0.1\right)$$
- step1: Add the numbers:
  $$626.5\times 1.1$$
- step2: Multiply the numbers:
  $$689.15$$
Now, let's summarize the calculations step by step:

1. **Future Value of Initial Deposit:**
   $$
   FV_1 = 1500(1 + 0.10)^3 = 1996.5
   $$

2. **Future Value of Second Deposit:**
   $$
   FV_2 = 3000(1 + 0.10)^2 = 3630
   $$

3. **Total Amount Before Withdrawal:**
   $$
   Total = FV_1 + FV_2 = 1996.5 + 3630 = 5626.5
   $$

4. **Balance After Withdrawal:**
   $$
   Balance\_after\_withdrawal = Total - 5000 = 5626.5 - 5000 = 626.5
   $$

5. **Amount Left After One Year:**
   $$
   Amount\_left = Balance\_after\_withdrawal(1 + 0.10) = 626.5 \times 1.10 = 689.15
   $$

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

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 .

Upstudy AI Solution

Answer

Solution

Step 1: Future Value of Initial Deposit

Step 2: Future Value of Second Deposit

Step 3: Total Amount Before Withdrawal

Step 4: Balance After Withdrawal

Step 5: Amount Left After One Year

Step 1 Calculation:

Step 2 Calculation:

Step 3 Calculation:

Step 4 Calculation:

Step 5 Calculation:

Extra Insights

Related Questions

Latest Economics Questions

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 .

Upstudy AI Solution

Answer

Solution

Step 1: Future Value of Initial Deposit

Step 2: Future Value of Second Deposit

Step 3: Total Amount Before Withdrawal

Step 4: Balance After Withdrawal

Step 5: Amount Left After One Year

Step 1 Calculation:

Step 2 Calculation:

Step 3 Calculation:

Step 4 Calculation:

Step 5 Calculation:

Extra Insights

Related Questions

Latest Economics Questions

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 .