HOW LONG WILL IT TAKE TO LOSE HALF OF YOUR 40000 INVESTMENT

HOW LONG WILL IT TAKE TO LOSE HALF OF YOUR $40,000 INVESTMENT @ 3 1/4 %, COMPOUNDED CONTINUOUSLY? YOU INVEST $14,000 IN AN ACCOUNT WHICH PAYS INTEREST COMPOUNDED CONTINUOUSLY. IF YOU WANT THE ACCOUNT TO CONTAIN $20,00 AFTER 8 YEARS, WANT INTEREST RATE IS NEEDED?(3 DECIMAL PERCENTAGE RATE) AT WHAT PERCENTAGE (TO 3 DECIMALS) MUST YOU INVEST $8,000 TO RENT $12,000 IN 6 YEARS? (COMPOUNDED CONTINUOUSLY)

Solution

A=P e^-rt

Here P=40000

A=1/2 of 40000=20000

r = 13/4%= .0325

20000=40000e^-.0325t

.5= e-^.0325t

Taking ln on both sides

ln.5/-.0325=t

t=21.328