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?

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.

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.)