- A seven-year, $10,000 promissory note, dated May 1, 2007, withinterest at 12% compounded quarterly is discounted four years afterthe date of issue at 16% compounded semi-annually. What are theproceeds of the note?
- Find the nominal annual rate of interest compounded quarterlythat is equal to an effective rate of 19.25%
- $4,000 is due in five years. If money is worth 12% compoundedannually, what is the equivalent payment in two years that wouldsettle this debt?
- A 3-year term deposit of $5,000 earns 8.5% compoundedquarterly?
- What is the maturity value?
- How much interest did the deposit earn?
- A deposit of $5,000 earns interest at 4% compoundedsemi-annually. After three-and-a-half years, the interest rate ischanged to 4.5% compounded quarterly. How much is the account worthafter 7 years?
- Jan is saving for a new bike that will cost $800. She has $500,which she has invested at 7% compounded semi-annually. How manyyears will it be (approximately) until she has $800?
- How long will it take for money to double if it is compoundedquarterly at 6%?
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
- = 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)
- = -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
- = -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)
