Question

Compound interest In Exercise,$3000 is invested in an account at interest rate r,compounded continuously.Find the time required for the amount to (a) double and (b) triple.

r = 0.045

Answer 1

(a) t = 15.40 years

(b) t = 24.41 years

Explanation:

The expression that describes continuous compounding is:

`FV = P*e^(rt)`

The principal (P) is $3,000 invested at a rate r=0.045.

a) The time required for the amount to double (FV =$6,000) is:

`6,000 = 3,000*e^(0.045t)\\0.045t*ln(e)=ln((6,000)/(3,000))\\ t=15.40\ years`

a) The time required for the amount to triple (FV =$9,000) is:

`9,000 = 3,000*e^(0.045t)\\0.045t*ln(e)=ln((9,000)/(3,000))\\ t=24.41\ years`