to make a balloon payment (large single payment) of $29,367.71 in 10 years. T on payment, you will make annual payments into a fund paying 3%. How much ayment be in order to satisfy the balloon payment when it is due?
to make a balloon payment (large single payment) of $29,367.71 in 10 years. T on payment, you will make annual payments into a fund paying 3%. How much ayment be in order to satisfy the balloon payment when it is due?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![**Title: Balloon Payment Preparation for Contract for Deed**
**Introduction:**
When purchasing a house through a contract for deed, it's essential to plan for all types of payments. In addition to regular monthly payments, there might be a requirement for a balloon payment, which is a large single payment due after a specific period. Proper financial planning is crucial to ensure that you meet this obligation.
**Scenario Explanation:**
Consider you have purchased your house with the following requirements:
- A balloon payment of $29,367.71 is due in 10 years.
- An annual fund payment earns an interest rate of 3%.
**Objective:**
To ensure you can make the balloon payment on time, determine how much should you deposit annually into the fund.
**Calculating Annual Payments:**
To find out the annual payment needed to accumulate $29,367.71 in 10 years with an interest rate of 3%, we can use the formula for the future value of an ordinary annuity:
\[ FV = P \left( \frac{(1 + r)^n - 1}{r} \right) \]
Where:
- \( FV \) is the future value ($29,367.71),
- \( P \) is the annual payment,
- \( r \) is the annual interest rate (0.03),
- \( n \) is the number of periods (10 years).
**Step-by-Step Solution:**
1. Rearrange the formula to solve for \( P \):
\[ P = \frac{FV \cdot r}{(1 + r)^n - 1} \]
2. Plug in the values:
\[ P = \frac{29,367.71 \cdot 0.03}{(1 + 0.03)^{10} - 1} \]
3. Calculate \( (1 + 0.03)^{10} \):
\[ (1 + 0.03)^{10} \approx 1.3439 \]
4. Subtract 1 from 1.3439:
\[ 1.3439 - 1 \approx 0.3439 \]
5. Multiply $29,367.71 by 0.03:
\[ 29,367.71 \cdot 0.03 \approx 881.0313 \]
6. Finally, divide the product by 0.3439:
\[ \frac{881.031](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdd4dcc1e-8f3e-4441-96ca-9bc187757338%2F4042fb8c-1299-450f-aedc-f2b764bdb380%2F5ze1cyj_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Balloon Payment Preparation for Contract for Deed**
**Introduction:**
When purchasing a house through a contract for deed, it's essential to plan for all types of payments. In addition to regular monthly payments, there might be a requirement for a balloon payment, which is a large single payment due after a specific period. Proper financial planning is crucial to ensure that you meet this obligation.
**Scenario Explanation:**
Consider you have purchased your house with the following requirements:
- A balloon payment of $29,367.71 is due in 10 years.
- An annual fund payment earns an interest rate of 3%.
**Objective:**
To ensure you can make the balloon payment on time, determine how much should you deposit annually into the fund.
**Calculating Annual Payments:**
To find out the annual payment needed to accumulate $29,367.71 in 10 years with an interest rate of 3%, we can use the formula for the future value of an ordinary annuity:
\[ FV = P \left( \frac{(1 + r)^n - 1}{r} \right) \]
Where:
- \( FV \) is the future value ($29,367.71),
- \( P \) is the annual payment,
- \( r \) is the annual interest rate (0.03),
- \( n \) is the number of periods (10 years).
**Step-by-Step Solution:**
1. Rearrange the formula to solve for \( P \):
\[ P = \frac{FV \cdot r}{(1 + r)^n - 1} \]
2. Plug in the values:
\[ P = \frac{29,367.71 \cdot 0.03}{(1 + 0.03)^{10} - 1} \]
3. Calculate \( (1 + 0.03)^{10} \):
\[ (1 + 0.03)^{10} \approx 1.3439 \]
4. Subtract 1 from 1.3439:
\[ 1.3439 - 1 \approx 0.3439 \]
5. Multiply $29,367.71 by 0.03:
\[ 29,367.71 \cdot 0.03 \approx 881.0313 \]
6. Finally, divide the product by 0.3439:
\[ \frac{881.031
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