Find the savings plan balance after 18 months with an APR of 8% and monthly payments of $150. ..….…. The balance is $ (Do not round until the final answer. Then round to the nearest cent as needed.)
Find the savings plan balance after 18 months with an APR of 8% and monthly payments of $150. ..….…. The balance is $ (Do not round until the final answer. Then round to the nearest cent as needed.)
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
Find the savings plan balance after 18 months with an apr of 8% and monthly payments of $150
![### Savings Plan Balance Calculation
#### Problem Statement:
**Objective:**
Find the savings plan balance after 18 months with an APR of 8% and monthly payments of $150.
---
#### Solution:
**Formula:**
The balance can be calculated using the future value of an annuity formula for compound interest:
\[ FV = P \times \left( \frac{(1 + r/n)^{nt} - 1}{r/n} \right) \]
Where:
- \( P \) = monthly payment
- \( r \) = annual interest rate (APR)
- \( n \) = number of times interest is compounded per year
- \( t \) = number of years
In this problem:
- \( P = 150 \)
- \( r = 0.08 \) (8% APR)
- \( n = 12 \) (since interest is compounded monthly)
- \( t = 1.5 \) (18 months is 1.5 years)
**Calculation Steps:**
1. Compute the monthly interest rate (\( r/n \)):
\[ r/n = 0.08/12 = 0.006666... \]
2. Compute the number of total payments (\( nt \)):
\[ nt = 12 \times 1.5 = 18 \]
3. Plug these values into the formula and calculate the future value.
**Result:**
The balance is \( \text{\S} \) ____
*(Do not round until the final answer. Then round to the nearest cent as needed.)*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9df0b4c-201f-409f-8e9a-9b9d50dcd48e%2F4d26f719-a059-4935-8e6e-4730436566d6%2Fs9q12e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Savings Plan Balance Calculation
#### Problem Statement:
**Objective:**
Find the savings plan balance after 18 months with an APR of 8% and monthly payments of $150.
---
#### Solution:
**Formula:**
The balance can be calculated using the future value of an annuity formula for compound interest:
\[ FV = P \times \left( \frac{(1 + r/n)^{nt} - 1}{r/n} \right) \]
Where:
- \( P \) = monthly payment
- \( r \) = annual interest rate (APR)
- \( n \) = number of times interest is compounded per year
- \( t \) = number of years
In this problem:
- \( P = 150 \)
- \( r = 0.08 \) (8% APR)
- \( n = 12 \) (since interest is compounded monthly)
- \( t = 1.5 \) (18 months is 1.5 years)
**Calculation Steps:**
1. Compute the monthly interest rate (\( r/n \)):
\[ r/n = 0.08/12 = 0.006666... \]
2. Compute the number of total payments (\( nt \)):
\[ nt = 12 \times 1.5 = 18 \]
3. Plug these values into the formula and calculate the future value.
**Result:**
The balance is \( \text{\S} \) ____
*(Do not round until the final answer. Then round to the nearest cent as needed.)*
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