Math Problem Statement
Jonathan and Agustina have a new grandson. How much money should they invest now so that he will have $79,000 for his college education in 18 years? The money is invested at 7.55% compounded quarterly
Solution
To calculate how much Jonathan and Agustina should invest now, we can use the present value formula for compound interest:
Where:
- is the present value (the amount they should invest now),
- is the future value (the amount they want in the future, $79,000),
- is the annual interest rate (7.55% or 0.0755 as a decimal),
- is the number of times the interest is compounded per year (quarterly means ),
- is the number of years the money will be invested (18 years).
Plugging in the values:
- ,
- ,
- ,
- .
Let me calculate this for you.Jonathan and Agustina should invest approximately $20,555.21 now in order to have $79,000 in 18 years for their grandson's college education, assuming an interest rate of 7.55% compounded quarterly.
Would you like further details on the calculation, or do you have any questions?
Here are 5 related questions you might consider:
- How does changing the interest rate affect the required investment?
- What happens if the interest is compounded monthly instead of quarterly?
- How much would the investment be worth after 10 years instead of 18 years?
- What if they wanted to withdraw the money over 4 years instead of as a lump sum?
- How does inflation affect the real value of the $79,000 in 18 years?
Tip: Compounding frequency (quarterly, monthly, etc.) significantly impacts how much you need to invest initially.
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Math Problem Analysis
Mathematical Concepts
Compound Interest
Present Value Calculation
Formulas
PV = FV / (1 + r/n)^(nt)
Theorems
Compound Interest Formula
Suitable Grade Level
Grades 11-12
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