Find the accumulated present value of an investment over a 8 year period if there is a continuous money flow of $11,000 per year and the interest rate is 1.6% compounded continuously.

Answer 1

The discrete case of compounded interest is A = P(1+r/n)^nt, where n is the number of compounding periods per year, t is the number of years, P is the principal, and r is the interest rate. The continuous case can be found by taking the limit n → ∞. This gives A = Pe^rt.

If we have a flow of P dollars each year then after N years we have A = P + Pe^r + Pe^2r + Pe^3r + ... + Pe^Nr. This can be simplified using the expression for a geometric series: A = P(e^(N+1)r-1)/(e^r-1)