Financial Calculations - Prof. Richard B. Goldstein

Compound Interest

 Example
Amount: A = P*(1 + r)n where r = i/k and n = k*t
Eff. Rate: ER = (1 + r)n - 1
where P = principal, r = interest per period, n = no. of periods

P = Principal ($)
 i = Annual Rate of Interest (%)
 k = No. of periods per year
 t = Years
A = Amount ($)
 ER = Effective Annual Rate (%)

Mortgage Payments
 
Example
Monthly Payment: R = P * i / (1 - (1 + i)-n) where i = r/12 and n =12*t
Debt Balance after k payments: D = P * (1 + i)k - R * ((1 + i)k - 1)/i)
where P = principal, r = interest rate per period, n = no. of periods,  and
k = no. of payments
P = Principal ($)
 r = Annual Rate of Interest (%)
 t = Years
 k = No. of Payments
R = Monthly Payment ($)
 D = Debt after K payments ($)

Accelerating Mortgage Payments

Suppose one decides to pay more than the monthly payment shown
above. How many months will it take until the mortgage is paid off?

  m= ln[x/(x - Pi)] / ln (1 + i)

P =  Principal ($)
 r = Annual Rate of Interest (%)
 x = Monthly Payment ($)
m = No. of Payments

Future Value of an Annuity

Example
Future Value: FV = R * ((1 + i)n - 1)/i)
where P = annual payment, r = rate of interest, k= no. of periods per year.
R = P/k, i = r/k and n = kt = no. of payments
P = Annual Payment ($)
 r  = Annual Rate of Interest (%)
 k = Number of Periods per Year
 t = Number of Years
FV = Future Value of Annuity ($)


More: Retirement Calculations

Return to: Miscellaneous