Exponential function

Question

Write a formula for the quantity described.

The balance in an interest-bearing bank account, if the balance triples in 18 years.

Let B0 be the initial balance and t be the number of years.

Answer 1

3Bo= Boe^18r

3= e^18r

ln3 = 18r

r = ln3/18

r= 1.0986/18=0.061034

= about 6.1% interest rate compounded continuously

A = Bo(e^.061(18)

A =Bo(e^1.0986)

A = about Bo(e^1.1)

or

3Bo = Bo(1 + r/n)n^t where n=1 = number of times compounded per year

3 = (1+r)^t

3= (1+r)^18

1+r = 3^(1/18)

r = -1 + 1.0629

r = about 0.063

r = about 6.3% compounded annually

A = Bo(1+.063)^18

for 1<n<infinity

the rate of interest is

6.1% < r < 6.3%

A = Bo(1+r/n)^18n with n typically daily, monthly, quarterly or annual compounding, with n=365, 12, 4 or 1