Math Problem Statement
using a TI BA II Plus Calculator Olivia plans to contribute $800.00 at the start of every 3 months to an investment that earns 8.75% compounded quarterly. If Olivia starts contributing on her 29th birthday, how much will she accumulate by her 44th birthday? Assume she doesn't make a contribution on her 44th birthday. Future Value:
Solution
To solve this problem using a TI BA II Plus calculator, we need to apply the formula for the future value of an ordinary annuity since Olivia is making contributions at regular intervals (every 3 months) into an account that earns interest compounded quarterly.
Variables:
- PMT (Payment): 800 (since she contributes $800 at the start of every quarter)
- Interest Rate (I/Y): 8.75% annually, compounded quarterly.
- Number of Periods (N): The number of quarters between her 29th and 44th birthdays.
- Future Value (FV): This is what we are solving for.
Steps to Solve:
-
Identify the number of quarters:
- Olivia is contributing from her 29th birthday until her 44th birthday. This is 15 years.
- Since contributions are made quarterly, there are 4 quarters per year.
-
Set the interest rate per period (I/Y):
- The annual interest rate is 8.75%, but it’s compounded quarterly, so the interest rate per quarter is:
-
Set PMT:
- Olivia contributes $800 at the start of each quarter. Since it's an annuity due (payments made at the start of each period), we need to set the calculator to this mode.
-
PV (Present Value):
- Olivia is not starting with any initial amount, so the present value is 0.
-
FV:
- We will calculate this.
Calculator Settings:
-
Set the calculator to BGN (beginning) mode because the payments are made at the start of the period.
- Press
2nd
→BGN
→2nd
→SET
to switch to Begin mode.
- Press
-
Input the following values into the calculator:
- N = 60 (number of quarters)
- I/Y = 2.1875 (quarterly interest rate)
- PMT = -800 (the payment is outflow, hence negative)
- PV = 0 (no initial investment)
-
Compute the future value:
- Press
CPT
→FV
.
- Press
Let's calculate this.The future value of Olivia's investment by her 44th birthday, given her quarterly contributions of $800 and an interest rate of 8.75% compounded quarterly, will be approximately $99,529.43.
Would you like further details or have any questions?
Here are five related questions you could explore:
- How would the future value change if Olivia contributed monthly instead of quarterly?
- What if the interest rate increased to 10% annually—how much would she accumulate?
- How much would Olivia need to contribute quarterly to reach $120,000 by her 44th birthday?
- What is the total amount of interest earned over the 15 years?
- How would the future value change if contributions were made at the end of each period instead?
Tip: Always ensure you are in the correct mode (Begin/End) on your financial calculator, as it affects how payments are treated!
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Math Problem Analysis
Mathematical Concepts
Annuity
Compound Interest
Future Value
Time Value of Money
Formulas
Future Value of an Annuity Due: FV = PMT * [(1 + r)^n - 1] * (1 + r) / r
Quarterly Interest Rate: r = Annual Interest Rate / 4
Theorems
Time Value of Money
Annuity Due
Suitable Grade Level
College Level / Advanced High School
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