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How many years will it take for the business owner to save GH60,000 by contributing GH500 monthly at an 8% annual interest rate?
How many years will it take for the business owner to save GH60,000 by contributing GH500 monthly at an 8% annual interest rate?
If Sandra contributes GH630 at the end of each month for 20 years at an 8% interest compounded semiannually, what will be the approximate future value of her retirement account?
If Sandra contributes GH630 at the end of each month for 20 years at an 8% interest compounded semiannually, what will be the approximate future value of her retirement account?
What is the formula to find the term of an ordinary annuity based on the future value?
What is the formula to find the term of an ordinary annuity based on the future value?
How long will it take Rosemary to save $300,000 by contributing $10,000 monthly at a 15% interest rate compounded monthly?
How long will it take Rosemary to save $300,000 by contributing $10,000 monthly at a 15% interest rate compounded monthly?
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What is the current value of an annuity of $7,500 paid at the end of each half-year for 10 years at a 9% interest rate compounded annually?
What is the current value of an annuity of $7,500 paid at the end of each half-year for 10 years at a 9% interest rate compounded annually?
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What is an annuity?
What is an annuity?
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Which of the following describes a contingent annuity?
Which of the following describes a contingent annuity?
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In the formula for the future value of an annuity, which variable represents the total number of payment periods?
In the formula for the future value of an annuity, which variable represents the total number of payment periods?
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What happens to the future value of an ordinary annuity if the interest rate increases?
What happens to the future value of an ordinary annuity if the interest rate increases?
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If you invested $1,000 at an annual interest rate of 7% compounded quarterly for 3 years, what would be the accumulation considering quarterly compounding?
If you invested $1,000 at an annual interest rate of 7% compounded quarterly for 3 years, what would be the accumulation considering quarterly compounding?
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Which of the following is a characteristic of a perpetuity?
Which of the following is a characteristic of a perpetuity?
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What does the term 'ordinary annuity' refer to?
What does the term 'ordinary annuity' refer to?
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The formula for calculating future value of an ordinary annuity is derived from which principle?
The formula for calculating future value of an ordinary annuity is derived from which principle?
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What is the formula for the future value (FV) of an ordinary annuity with $n$ terms of payment?
What is the formula for the future value (FV) of an ordinary annuity with $n$ terms of payment?
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If Adam contributes $1200 yearly at an interest rate of 6% compounded annually, what will be his total FV by age 65?
If Adam contributes $1200 yearly at an interest rate of 6% compounded annually, what will be his total FV by age 65?
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What would be the quarterly interest rate if the annual interest rate is 4%?
What would be the quarterly interest rate if the annual interest rate is 4%?
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Which values should be used to determine the total amount paid by Eben until age 50 if he contributes $200 monthly at an interest rate of 3% compounded semiannually?
Which values should be used to determine the total amount paid by Eben until age 50 if he contributes $200 monthly at an interest rate of 3% compounded semiannually?
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In Kelvin's scenario, how large will the education fund be when his son starts college at age 18?
In Kelvin's scenario, how large will the education fund be when his son starts college at age 18?
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How is the future value formula for an ordinary annuity expressed using tables?
How is the future value formula for an ordinary annuity expressed using tables?
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What is the correct method for obtaining the current value of an ordinary annuity?
What is the correct method for obtaining the current value of an ordinary annuity?
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If an ordinary annuity has monthly contributions of $300, what would be the semiannual contribution amount?
If an ordinary annuity has monthly contributions of $300, what would be the semiannual contribution amount?
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What is the formula used to calculate the current value of an ordinary annuity?
What is the formula used to calculate the current value of an ordinary annuity?
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How would you determine the monthly interest rate if the annual interest rate is 6.5%?
How would you determine the monthly interest rate if the annual interest rate is 6.5%?
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If a man receives $500 a month for 10 years at an interest rate of 6.5%, what is the term in months for this annuity?
If a man receives $500 a month for 10 years at an interest rate of 6.5%, what is the term in months for this annuity?
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For an annuity of $3,750 paid quarterly for 7 years at an interest rate of 8%, what is the total number of payments?
For an annuity of $3,750 paid quarterly for 7 years at an interest rate of 8%, what is the total number of payments?
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What is the formula to find the payment amount (A) of an ordinary annuity when the current value (CV) is known?
What is the formula to find the payment amount (A) of an ordinary annuity when the current value (CV) is known?
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If Jim deposited $18,000 in an account with a 12% interest rate compounded semiannually for 6 years, what payment will his son receive?
If Jim deposited $18,000 in an account with a 12% interest rate compounded semiannually for 6 years, what payment will his son receive?
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What is the quarterly interest rate if the annual interest rate is 8%?
What is the quarterly interest rate if the annual interest rate is 8%?
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In the context of future value calculations, what does the term $(1 + r)^{n} - 1$ relate to?
In the context of future value calculations, what does the term $(1 + r)^{n} - 1$ relate to?
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Study Notes
Introduction to Actuarial Science - Week 2
- Actuarial science focuses on calculating and managing financial risks.
- Actuaries apply mathematical and statistical principles to assess and manage risk in areas like insurance, pensions, and investments.
- Core areas of actuarial application include definitions and scope, actuarial roles, simple and compound interest calculations, annuities, and future and present value calculations.
Simple and Compound Interest
- Simple interest calculates interest only on the principal amount.
- Compound interest calculates interest on both the principal and the accumulated interest.
- Compound interest formulas determine accumulated amounts based on different compounding frequencies (annual, quarterly, monthly, weekly).
Annuities
- An annuity is a series of equal payments or receipts made at fixed intervals of time.
- Examples include periodic savings deposits, mortgages, life insurance premiums, and social security deductions.
- Annuity types include term, annuity certain, contingent annuity, and perpetuity.
Future Value of an Ordinary Annuity
- Future value is the accumulated amount a series of equal payments will reach after a specific time period.
- The formula for future value (FV) is A[(1+r)^n - 1] / r, where A represents the periodic payment, r is the interest rate, and n is the number of payment periods.
- Calculations for future value can be found with tables.
Current Value of an Ordinary Annuity
- Current value is the present worth of a series of future payments.
- The formula for the current value (CV) is A[1 - (1 + r)^-n] / r, where A represents the periodic payment, r is the interest rate, and n is the number of payment periods.
- Calculations for current value can be found with tables.
Finding the Payment of an Ordinary Annuity (A)
- Formulas for finding periodic payments (A) given the future value (FV) or current value (CV) of an ordinary annuity are provided.
- The formulas use the respective future value and current value formulas.
Finding the Term of an Ordinary Annuity
- Formulas for determining the number of payment periods (n) given the future or current value of an ordinary annuity are presented.
- The formulas involve the use of logarithms (ln) and can be used with future value (FV) or current value (CV).
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Description
Explore the second week of Introduction to Actuarial Science, focusing on key concepts such as simple and compound interest, as well as annuities. Understand how actuaries assess financial risks and the importance of calculations in various financial applications. This quiz will test your knowledge on fundamental principles critical for anyone pursuing a career in actuarial science.
