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 hundredth of a year how long it takes for an amount of money to double if interest is compounded continuously at 3.1%.

Round to the nearest tenth.

Question

Jerry Hopkins

Mathematics

26 August, 22:55

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 hundredth of a year how long it takes for an amount of money to double if interest is compounded continuously at 3.1%.

Round to the nearest tenth.

+2

Answers (2)

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Cowan · Answer 1

A=future amount

P=present amount

r=rate in decimal

t=time in years

when A=2P, then that is double

A=Pe^ (rt)

2P=Pe^ (rt)

divide by P

2=e^ (rt)

r=3.1% or 0.031 solve for t

2=e^ (0.031t)

take the ln of both sides

ln (2) = 0.031t

divide both sides by 0.031

(ln (2)) / 0.031=t

use calculator

22.359=t

round to tenth

22.4 years to double

Marshmallow · Answer 2

It will take approximately 1.04 years to double the principal amount.