Question

The interest equation
A
=
P
e
r
t
can be used to determine the final value, A, of a continuously compounded interest-bearing account for t years after an initial amount of money, P, was deposited. If $1,830 is the initial deposit in an account that earns 3.4% interest, which expression can be used to determine the number of years required for the value of the account to triple?


log
3
0.034


ln
3
0.034


log
5490
0.034
(
ln
1830
)


ln
5490
0.034
(
log
1830
)

Answer 1

Using A = Pe^{rt}, set 3P = P e^{0.034t} → 3 = e^{0.034t}. Take natural log: ln 3 = 0.034 t, so t = (ln 3)/0.034.

(So choose: ln 3 / 0.034; numerically ≈ 32.31 years.)