Compound Interest How much money should you deposit into a c

Compound Interest. How much money should you deposit into a certificate of deposit that pays 4% a year compounded continuously to have $90,000 in the account in 18 years? $ _______

Solution

The formula for continuous compoundiing is A = Pe^rt , where P is the initial amount, r is the rate of interest in decimals, t is the number of years and A is the maturity amount. Here, A = $90000, r = 0.04 and t = 18. Therefore, we have 90000 = Pe^0.4*18 = Pe^0.72. Therefore, P = 90000/e^0.72 = 90000/2.05443321 = $ 43807.70 ( on rounding off to the nearest cent).The answer is $ 43807.70.