Part I SimpleAnnuities

1. Len Stine is saving for his retirement 15 years from now, andhas set up a savings plan into which he will deposit $500 at theend of each month for the next 15 years. Interest is at 6%compounded monthly.
2. 1. How much will be in Mr. Stine’s account on the date of hisretirement?

2. How much will Mr. Stine have contributed.

3. How much is interest?

2. Jill is planning to retire in eight years, and wants to receive$300 a month for 15 years after she retires to supplement herpension, beginning one month after her retirement date. How muchwill she have to invest now, at 6% compounded monthly, to be ableto achieve her goal?

3. What amount would be required today to pay an annuity of $72 amonth for 15 years, if money earns 4% compounded monthly?

Financial Mathematics

FORMULA SHEET

i = j / m

I = Prt

t = I / Pr

P = I / rt

S = P(1 + i)ⁿ

f = (1 + i)^m - 1

n = ln (S / P)

ln (1 + i)

Sn = R[(1 + p)ⁿ - 1]

p

R=          Sn

[(1 + p)ⁿ - 1] / p

14. = ln [1 + pSn/R] ln (1 + p)

Sn(due) = R[(1 + p)ⁿ - 1](1+ p)

p

n = ln [1 +[pSn(due) / R(1 + p)] ln(1 + p)

14. = -ln[1 - (p[1 + p]^dAn(def))/R] ln(1 + p)

An(def) = R [1 - (1+ p)^-n] p(1 + p)^d

A = R / p

m = j / i

S = P(1 + rt)

r = I / Pt

P = S / (1 + rt) = S(1 + i)^-n

c = # of compoundings/# of payments

p = (1 + i)^c - 1

i = [S / P] ^1/n - 1

An = R[1 - (1 + p)^-n]

p

R =          An

[1 - (1 + p)^-n] / p

14. = -ln [1 - pAn/R] ln (1 + p)

An(due) = R[1 - (1 + p)^-n](1 + p)

p

n = -ln[1 -[pAn(due) / R(1 + p)] ln(1 + p)

d = -ln{R[1-(1 +p)^-n] / pAn(def)} ln(1 + p)

Sn(def) = Sn

A(due) = (R / p)(1 + p)