Victoria deposits money into an account bearing 5 38 annual

Victoria deposits money into an account bearing 5 3/8% annual interest compounded continuously. Calculate the following round both answers to the nearest tenth of a year. How long will it take her money to triple? How long will it take her money to sextuple?

Solution

A = P(1+r/n)^(nt)

where A=amount, P=principle money, r=rate, n=compound frequency, t=time in years

(a) A = 3*P

Hence, 3P = P(1+43/800)^(1*t)

3 = (843/800)^t

ln₃(3) = ln₃(843/800)^t

hence, 1 = t * ln₃(843/800)

so, t = 1/ln₃(843/800) = 1/0.047655784369 = 20.9838116 years

(b) now, amount has to be equal to 6 times the original money.

hence, A = 6P

6P = P(1+43/800)^(1*t)

so,

6 = (843/800)^t

ln₆(6) = ln₆(843/800)^t

hence, 1 = t * ln₆(843/800)

so, t = 1/ln₆(843/800) = 1/0.029220010405=34.2231227 years