Math Problem Statement
Match each description to the type of financial situation it describes.
Group of answer choices
Only earns interest on the initial deposit
[ Choose ] Compound Interest Annuity Simple Interest Amortized Loan Payout Annuity
Single initial deposit, but earns interest on principal and interest
[ Choose ] Compound Interest Annuity Simple Interest Amortized Loan Payout Annuity
Interest on principal and interest, but with regular deposits
[ Choose ] Compound Interest Annuity Simple Interest Amortized Loan Payout Annuity
Interest on principal and interest, but with regular withdrawals
[ Choose ] Compound Interest Annuity Simple Interest Amortized Loan Payout Annuity
Buying a home
[ Choose ] Compound Interest Annuity Simple Interest Amortized Loan Payout Annuity
Solution
Here are the descriptions and corresponding financial situations:
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Only earns interest on the initial deposit
Answer: Simple Interest- Simple interest is calculated only on the initial principal, not on accumulated interest.
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Single initial deposit, but earns interest on principal and interest
Answer: Compound Interest- Compound interest includes interest on the initial principal and on the interest already earned.
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Interest on principal and interest, but with regular deposits
Answer: Annuity- An annuity involves regular deposits and earns interest on both the principal and any accumulated interest.
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Interest on principal and interest, but with regular withdrawals
Answer: Payout Annuity- A payout annuity allows for regular withdrawals while continuing to earn interest on the remaining principal.
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Buying a home
Answer: Amortized Loan- An amortized loan is typically used for large purchases like homes, where the loan is paid off over time with regular payments that include both interest and principal.
Would you like more details or have any further questions?
Here are 5 related questions:
- What is the formula for calculating simple interest?
- How does compound interest differ when compounded annually versus monthly?
- What are the advantages of an annuity compared to a lump-sum investment?
- How does a payout annuity help in retirement planning?
- How is the monthly payment for an amortized loan calculated?
Tip: Compound interest grows faster than simple interest because it earns interest on interest!
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Math Problem Analysis
Mathematical Concepts
Interest Calculation
Simple Interest
Compound Interest
Annuities
Amortized Loans
Formulas
Simple Interest: I = P * r * t
Compound Interest: A = P(1 + r/n)^(nt)
Annuities: FV = P * [(1 + r)^nt - 1] / r
Amortized Loan: PMT = [P * r * (1 + r)^n] / [(1 + r)^n - 1]
Theorems
Compound Interest Theorem
Time Value of Money
Suitable Grade Level
Grades 9-12
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