Please help me with this

Question

A bank account is growing by 2.2% per year. Find the doubling time.

Round your answer to the nearest integer.

The doubling time is years.

Answer 1

Given: Bank account is growing by 2.2% per year.

Find: Doubling time. Round answer to nearest integer.

t = time in years

A = Amount

A0 = Original Amount

r = rate

r = 2.2%

r = 2.2 per 100

r = 2.2/100

r = .022

A = A0( 1 + r )^(t)

A = A0(1 + .022)^(t)

A = A0(1.022)^(t)

When the Amount is Doubled

we have:

2*A0 = A0(1.022)^(t) Divide both sides by A0

2 = (1.022)^(t)

ln(2) = t*ln(1.022)

t = [ ln(2) ] / [ ln(1.022) ]

t = 31.852 years

t = 32 years Doubling time.