A principal P is to be invested at continuous compound inter

A principal P is to be invested at continuous compound interest of 9% to yield $50,000 in 20 years. What is the approximate value of P to be invested?

Solution

The formula for the continuous compounding of interest is A = Pe^rt, where P is the principal, r is the rate of interest in decimals, t is the time in years and A is the future value. Here, A = $ 50000, t = 20 and r = 0.09. Then, on substituting these values in the formula, we get 50000= Pe^0.09*20 = Pe^1.80. Hence P = 50000/e^1.80= 50000/6.04964746441 = $ 8264.94 ( on rounding off to the nearest cent). The answer is P = $ 8264.94.