The amount of money in an account with continuously compounded interest is given by the formula a = pert, where p is the principal, r is the annual interest rate, and t is the time in years. calculate to the nearest tenth of a year how long it takes for an amount of money to double if interest is compounded continuously at 7.5%.

9 years

Step-by-step explanation:

The amount of money in an account with continuously compounded interest is given by the formula A = Pe^rt, where P is the principal, r is the annual interest rate, and t is the time in years

Initial amount invested is P  and when the amount of money doubles then A becomes 2P

A= 2P

P=P

r= 7.5%= 0.075

t=t

Now we use formula A=Pe^rt

Divide by P on both sides

To solve for t, take ln on both sides'

ln(2)= 0.075 *t

Divide by 0.075 on both sides

t= 9.24196

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