B13 Annuity Immediate - Accum. Value

Question 1

What is first principles?

Answer 1

Another way of saying sum the series

S = (a-ar^n)/(1-r)

The sum of geometric series equals the first term minus the what comes after the term you’re given in the series, divided by 1 minus what we multiply by each time.

Question 2

what does s angle n mean intuitively?

Answer 2

its the accumulated value of n payments at the time of the last payment

Question 3

what is the formula for s angle n? In other words, how do you find the accumlate value of n payments of k at the time of the last payment?

Answer 3

s angle n = a angle n * (1+i)^n = ((1+i)^n - 1)/i

Question 4

What Interest rate should you use for s angle n?

Answer 4

i should be interpreted as the effective rate of interest per payment period.

Question 5

How can we use grouping to express s angle 2n in terms of s angle n?

Answer 5

s angle 2n = s angle n * (1+i)^n + s angle n