Math Problem Statement
Calculate the amount of an annuity at the time of the last payment for each section. A) You deposit $1000 every year for 8 years at 3%/a compounded annually.
B) You pay $200 for 30 months. The interest rate is 6%/a compounded monthly.
Solution
To calculate the amount of an annuity at the time of the last payment, we will use the future value of an ordinary annuity formula. This formula is:
where:
- is the payment amount
- is the interest rate per period
- is the number of periods
A) Annual Deposits of $1000 for 8 Years at 3% Interest Compounded Annually
Given:
Using the formula:
First, calculate :
Now, apply the values:
So, the future value of the annuity at the time of the last payment is approximately $8893.30.
B) Monthly Payments of $200 for 30 Months at 6% Interest Compounded Monthly
Given:
Using the formula:
First, calculate :
Now, apply the values:
So, the future value of the annuity at the time of the last payment is approximately $6464.00.
Would you like further details or have any questions?
Here are some related questions you might want to ask:
- How do you calculate the present value of an annuity?
- What is the difference between an ordinary annuity and an annuity due?
- How does the compounding frequency affect the future value of an annuity?
- Can you explain the annuity formula in more detail?
- What are some common applications of annuities in finance?
Tip: Always double-check the compounding period and ensure the interest rate and periods align correctly (e.g., annual interest rate with monthly payments should be divided by 12).
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Math Problem Analysis
Mathematical Concepts
Finance
Compound Interest
Annuities
Formulas
Future Value of Annuity Formula
Theorems
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Suitable Grade Level
Advanced High School