Introduction to Actuarial Science - Week 2

The formula for finding the term of an annuity requires the future value, the annual interest rate, and the amount of the periodic payment.

The term of an ordinary annuity can be found using a formula that involves the natural logarithm.

To calculate the term of an annuity, at least three variables are required.

The amount of the periodic payment can be calculated using the formula for the future value of an annuity.

A perpetuity is an annuity where the end of the term is known and finite.

To find the term of an annuity, the future value is divided by the annual interest rate, and then the result is added to $1$.

A contingent annuity has a known starting date but an uncertain ending date, typically tied to an event like death.

An annuity certain is defined as an annuity where both the beginning and end of the term are known and set in advance.

Investments are the only examples of annuities, as they involve regular payments over time.

For a quarterly annuity with a term of one year, the last payment would be due at the beginning of the fourth quarter.

The formula for calculating the future value of an ordinary annuity is essentially the same as the formula for calculating the future value of a single lump sum investment.

If you were to invest $1,000 at an annual interest rate of 7% for 3 years, you would accumulate more money if the interest compounded monthly than if it compounded quarterly.

The future value of an annuity can be calculated using the formula $FV = PV(1 + r)^{t}$, where FV represents the future value, PV represents the present value, r represents the interest rate, and t represents the time period.

In the first quarter of an ordinary annuity, the future value is equivalent to the initial principal amount multiplied by $(1 + r)^3$.

The future value of an ordinary annuity with 'n' payment terms is calculated by adding the future values of each payment term.

If an ordinary annuity has an interest rate of 5% compounded annually, and the payment term is 10 years, the future value factor is calculated as (1 + 0.05)^10 - 1 / 0.05.

For a quarterly compounding ordinary annuity, the interest rate must be divided by 4 to obtain the quarterly interest rate.

If Adam contributes $1,200 annually to his retirement account for 40 years at an interest rate of 6% compounded annually, his total retirement fund will be approximately $185,714.36.

If Kelvin deposits $150 monthly into his son's education fund for 12 years, with an interest rate of 4% compounded quarterly, the son's education fund will be approximately $25,000 when he turns 18.

If Eben makes monthly payments of $200 for a mortgage with a 3% annual interest rate compounded semiannually for 25 years, the total amount he will have paid by the age of 50 will be approximately $88,419.39.

The future value formula for an ordinary annuity can be rewritten as FV = A * Sn ¬r, where Sn ¬r is the future value factor.

The monthly interest rate for a trust fund paying 6.5% compounded monthly is 0.0054.

To calculate the current value of an annuity with quarterly payments, you should use the formula $CV = A * 1/(1 + r)^{-n}$.

If an annuity pays $3,750 at the end of each quarter for 7 years at an interest rate of 8%, the total number of payments is 28.

The formula for future value (FV) of an ordinary annuity is $FV = A (1 + r)^n - 1$.

If Jim deposited $18,000 in his savings account, he would receive less than $1,800 as a semiannual payment at 12% interest compounded semiannually for 6 years.

Samantha's quarterly deposit for a $17,000 car at 8% interest compounded quarterly for 5 years should be calculated using the current value formula.

For the formula $CV = A * a_n¬_r$, the variable 'A' represents the current value.

The formula for calculating the payment (A) of an ordinary annuity is $A = CV * r / (1 - (1 + r)^{-n})$.