Math Problem Statement
Question content area top Part 1 (Compound annuity) What is the accumulated sum of each of the following streams of payments? a. $510 a year for 9 years compounded annually at 9 percent. b. $104 a year for 6 years compounded annually at 8 percent. c. $38 a year for 12 years compounded annually at 11percent. d. $23 a year for 5 years compounded annually at 4 percent. Question content area bottom Part 1 a. What is the accumulated sum of $510 a year for 9 years compounded annually at 9 percent? $ enter your response here (Round to the nearest cent.)
Solution
To calculate the accumulated sum of a stream of payments (a compound annuity), we use the future value of an annuity formula:
Where:
- = Future Value
- = Annual payment
- = Interest rate per period (as a decimal)
- = Number of years
Given for part (a):
Now, we compute:
Let's calculate. Given values for part (a) P = 510 # Annual payment r = 0.09 # Interest rate per year n = 9 # Number of years
Future Value calculation
FV_a = P * ((1 + r)**n - 1) / r FV_aThe accumulated sum for part (a) is $6,640.73 (rounded to the nearest cent).
Would you like me to proceed with the other parts (b, c, d)?
Here are five related questions to deepen understanding:
- How does increasing the interest rate affect the accumulated sum?
- What happens if payments are made semi-annually instead of annually?
- How does the number of years impact the future value of an annuity?
- Can this formula be applied to monthly deposits? If so, how?
- What is the difference between a future value annuity and a present value annuity?
Tip: The longer the time period and the higher the interest rate, the more significant the compound growth effect!
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Math Problem Analysis
Mathematical Concepts
Compound Annuity
Future Value of Annuity
Interest Calculations
Formulas
FV = P * ((1 + r)^n - 1) / r
Theorems
Future Value of Annuity Theorem
Suitable Grade Level
Grades 11-12
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