Question

Lee has invested $2800 in a venture company,he receives 6.5 % interest in a year,compounded continuously. how long will it take his money to double

Answer 1

`t=10.66\ years`

Explanation:

we know that

The formula to calculate continuously compounded interest is equal to

`A=P(e)^(rt)`

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

`t=?\ years\\ P=\$2,800\\A=\$5,600\\r=0.065`

substitute in the formula above

`5,600=2,800(e)^(0.065t)`

solve for t

simplify

`2=(e)^(0.065t)`

Apply ln both sides

`ln(2)=ln[(e)^(0.065t)]`

Apply property of logarithms

`ln(2)=(0.065t)ln(e)`

`ln(e)=1`

`t=ln(2)/(0.065)`

`t=10.66\ years`