Annuities

Question 1

a n | i (there should be a line over the n) Formula and PV or AV

Answer 1

( 1 - v^n ) / i PV Bonus: v + v^2 + … + v^n

Question 2

s n | i (there should be a line over the n) Formula and PV or AV

Answer 2

( ( 1 + i )^(n) - 1) / i AV Bonus: 1 + (1 + i) + (1 + i)^2 + … + (1 + i)^(n - 1)

Question 3

Definition difference between annuity-immediate and annuity-due?

Answer 3

Payments made under an ordinary annuity occur at the end of the period while payments made under an annuity due occur at the beginning of the period.

Question 4

Formula difference between annuity-immediate and annuity-due

Answer 4

Annuity immediate = annuity due * (1 + i)

Question 5

PV of m-year deferred n-year annuity-immediate

Answer 5

v^m * a n | i

Question 6

PV of m-year deferred n-year annuity-due

Answer 6

v^m * (a n | i) * (1 + i)

Question 7

PV of a perpetuity-immediate

Answer 7

1 / i

Question 8

PV of a perpetuity-due

Answer 8

1 / d

Question 9

What to do if payment period doesn’t equal interest period?

Answer 9

change interest period to an equivalent rate.

Question 10

PV of a annuity-immediate convertible m-nthly.

Answer 10

( i / i^(m) ) * a n|

Question 11

AV of a annuity-immediate convertible m-nthly.

Answer 11

( i / i^(m) ) * s n|

Question 12

PV of a annuity-due convertible m-nthly.

Answer 12

( d / d^(m) ) * a n|

Question 13

AV of a annuity-due convertible m-nthly.

Answer 13

( d / d^(m) ) * s n|

Question 14

PV of a annuity-immediate perpetuity convertible monthly

Answer 14

1 / ( i ^ (m) )

Question 15

PV of a annuity-due perpetuity convertible monthly

Answer 15

1 / (d ^ (m) )

Question 16

PV of an annuity-immediate arithmetic progression with payment P, P+Q, P+2Q, … P + (n-1)Q

Answer 16

( P * (a|n) ) + Q * (a|n - nv^n) / i

Question 17

PV of a perpetuity-immediate with payments 1, 2, 3, …

Answer 17

1 / (id) or (1/i) + (1/i^2)

Question 18

PV of a perpetuity-due with payments 1, 2, 3, …

Answer 18

1 / d^2

Question 19

PV of a annuity-immediate with payments n, n-1, n-2, …, 1

Answer 19

( n - an|i ) / i

Question 20

PV of an n-year annuity-immediate with payments 1, (1 + k), (1 + k)^2, …, (1 + k)^n-1

Answer 20

( 1 - ( (1 + k) / (1 + i) ) ^ n ) / (i - k)

Question 21

Level Continuous Annuity

Answer 21

integral with respect to n of v^t or (i / (force of interest) ) * a n|i

Question 22

Increasing Continuous Annuity

Answer 22