Question

A principal of $4600 is invested at 5.5% interest, annually. How many years will it take to accumulate $7000 or more in the account?

Answer 1

A = 7000
P = 4600
r = 5.5% = 5.5/100 = 0.055
n = 1
t = unknown

A = P*(1+r/n)^(n*t)
7000 = 4600*(1+0.055/1)^(1*t)
7000 = 4600*(1+0.055)^t
7000 = 4600*(1.055)^t
7000/4600 = [4600*(1.055)^t]/4600
1.52173913043478 = 1.055^t
Log[1.52173913043478] = Log[1.055^t]
Log[1.52173913043478] = t*Log[1.055]
Log[1.52173913043478]/Log[1.055] = t
t = Log[1.52173913043478]/Log[1.055]
t = 7.84176002044643

It will take at least 8 years.

Answer 2

Interest = PRT/100
Where
P = Principle (amount)
R = Rate
T = Time

$7000 - $4600 = $2600
$2600 = PRT/100
$2600 = ($7000)(5.5%)(T)/100
T = (($2600)(100))/($7000)(5.5%)
T = 6.75324 years
T ≈ 6.75 years (3s.f.)