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What is the main characteristic of an annuity certain?
What is the main characteristic of an annuity certain?
In the context of annuities, which of the following best describes perpetuity?
In the context of annuities, which of the following best describes perpetuity?
How would you calculate the future value of an ordinary annuity with a payment amount of A, an interest rate of r, and a term of n?
How would you calculate the future value of an ordinary annuity with a payment amount of A, an interest rate of r, and a term of n?
What does the term 'term of annuity' refer to?
What does the term 'term of annuity' refer to?
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Which type of annuity is characterized by payments that depend on a certain event?
Which type of annuity is characterized by payments that depend on a certain event?
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What is the formula used to calculate the future value of an ordinary annuity with 'n' payment terms?
What is the formula used to calculate the future value of an ordinary annuity with 'n' payment terms?
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In the example given, how much total will Adam have collected by age 65 if he contributes $1200 yearly at an interest rate of 6%?
In the example given, how much total will Adam have collected by age 65 if he contributes $1200 yearly at an interest rate of 6%?
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If Kelvin deposits $150 monthly at 4% interest compounded quarterly, how will the deposit amount change by the time his son turns 18?
If Kelvin deposits $150 monthly at 4% interest compounded quarterly, how will the deposit amount change by the time his son turns 18?
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How does Eben's interest rate of 3% compounded semiannually affect his total payments when he pays $200 monthly?
How does Eben's interest rate of 3% compounded semiannually affect his total payments when he pays $200 monthly?
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Which method can be used to calculate the future value of an ordinary annuity with greater ease?
Which method can be used to calculate the future value of an ordinary annuity with greater ease?
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Study Notes
Introduction to Actuarial Science - Week 2
- Actuarial science is a specialized branch of mathematics that uses mathematical and statistical methods to assess financial risks.
- Actuaries apply their skills to a wide range of financial areas like insurance, pensions, and investments.
- Core areas of actuarial application include the calculation and analysis of simple and compound interest.
- Simple interest calculations do not take into account compounding, as the interest is earned only on the principal.
- Compound interest calculates interest on the investment's principal alongside the accumulated interest.
Compound Interest Recap
- To calculate compounded interest the formula
A = P(1 + r/n)^(nt)is used. - A = the future value of the investment/loan, including interest
- P = the principal investment amount (the initial deposit or loan amount)
- r = the annual interest rate (decimal)
- n = the number of times that interest is compounded per year
- t = the number of years the money is invested or borrowed for
Annuities
- An annuity is a series of equal payments made at equal intervals.
- Annuities can be classified as; annuities certain, contingent and perpetuity.
- Annuity certain - the beginning and ending dates of the annuity are fixed.
- Contingent annuity - the ending date of the annuity is contingent on an event; for instance, the death of an insured.
- Perpetuity - the beginning of the annuity's term is fixed, but the ending is considered infinite.
- Examples of annuities include periodic savings, mortgages, life insurance premiums, and social security deductions.
Future Value of an Ordinary Annuity
- The future value of an ordinary annuity refers to the total accumulated value of a series of equal payments made at the end of each period.
- It is calculated using the formula
FV = A[(1 + r)n − 1]/r.- FV = future value
- A = periodic payment amount
- r = periodic interest rate
- n = number of periods
Current Value of an Ordinary Annuity
- The current value of an ordinary annuity, or present value of an annuity, is the current worth of a series of future payments.
- The formula is
CV = A[1 − (1 + r)−n]/r.- CV = Current value
- A = periodic payment amount
- r = periodic interest rate
- n = number of periods
Using Tables for Annuity Calculations
- Actuarial tables can be used to calculate future and present values using the appropriate formulas (e.g.,
FV=A*S,Cv=A*n).
Finding the Term of an Ordinary Annuity
- The term of an annuity (n) represents the duration for which equal payments are made, which is calculated with formulas using the natural logarithm function
-
n=ln[(FV × r + A)/A] /ln(1 + r)for future value
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n = ln(1 − (CV × r)/A)/ ln(1 + r)for present value
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Description
This quiz covers fundamental concepts in actuarial science, focusing on the applications of simple and compound interest. You will learn how these calculations are critical in assessing financial risks in various sectors, including insurance and investments. Test your understanding of the relevant formulas and principles.
