Part I Simple Annuities

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

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 her pension, beginning one month after her retirement date. How much will she have to invest now, at 6% compounded monthly, to be able to achieve her goal?

3. What amount would be required today to pay an annuity of $72 a month 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)