A students deposits 1500 pesos in a 9% compounded semi-annually account today.He intends to deposit another 3000 pesos at the end of two years. He plans to purchase in five years his favorite shoes worth 5000 pesos. calculate the money that will be left in his account one year after the purchase
A students deposits 1500 pesos in a 9% compounded semi-annually account today.He intends to deposit another 3000 pesos at the end of two years. He plans to purchase in five years his favorite shoes worth 5000 pesos. calculate the money that will be left in his account one year after the purchase
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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![**Problem Description:**
A student deposits 1500 pesos in a 9% compounded semi-annually account today. He intends to deposit another 3000 pesos at the end of two years. He plans to purchase in five years his favorite shoes worth 5000 pesos. Calculate the money that will be left in his account one year after the purchase.
**Explanation:**
To solve this problem, you will apply the formula for compound interest and account for additional deposits and withdrawals:
1. **Initial Deposit:**
- Principal (P) = 1500 pesos
- Annual interest rate (r) = 9%
- Compounded semi-annually: n = 2 times per year
- Time from initial deposit to shoe purchase: 5 years
2. **Additional Deposit:**
- Further deposit of 3000 pesos after 2 years
- Calculate the compound interest from the time of the second deposit to the purchase (3 years).
3. **Calculate Account Balance Before Purchase:**
- Use the compound interest formula:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
- Calculate interest and new balance after each deposit.
4. **Calculate Account Balance After Shoe Purchase:**
- Subtract the cost of shoes (5000 pesos) from the account balance after 5 years.
5. **Balance One Year After Purchase:**
- Calculate the compound interest on the remaining balance for one more year.
By following these steps, you will compute the final balance in the student's account.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b043e75-eaf3-4ce6-b93c-f1556947ca10%2F36fba5b0-cd69-4277-b8f5-48219cd9ed74%2F0p27ofe_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Description:**
A student deposits 1500 pesos in a 9% compounded semi-annually account today. He intends to deposit another 3000 pesos at the end of two years. He plans to purchase in five years his favorite shoes worth 5000 pesos. Calculate the money that will be left in his account one year after the purchase.
**Explanation:**
To solve this problem, you will apply the formula for compound interest and account for additional deposits and withdrawals:
1. **Initial Deposit:**
- Principal (P) = 1500 pesos
- Annual interest rate (r) = 9%
- Compounded semi-annually: n = 2 times per year
- Time from initial deposit to shoe purchase: 5 years
2. **Additional Deposit:**
- Further deposit of 3000 pesos after 2 years
- Calculate the compound interest from the time of the second deposit to the purchase (3 years).
3. **Calculate Account Balance Before Purchase:**
- Use the compound interest formula:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
- Calculate interest and new balance after each deposit.
4. **Calculate Account Balance After Shoe Purchase:**
- Subtract the cost of shoes (5000 pesos) from the account balance after 5 years.
5. **Balance One Year After Purchase:**
- Calculate the compound interest on the remaining balance for one more year.
By following these steps, you will compute the final balance in the student's account.
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