A principal of $ 3800 is invested at 5 % interest, compounded annually. How many years will it take to accumulate $ 7000 or more in the account?

Question

Write the smallest possible whole number answer.

Answer 1

Let's find out how long it will take to accrue $7000

 

A = p(1+r/n)^nt

A = final amount = 7000

p = principal = 3800

r = interest rate = .05

n = # times compounded per year = 1

t = time in years

 

7000 = 3800(1+.05/1)^1(t)

7000/3800 = 1.05^t

35/19 = 1.05^t

 

Take log of both sides

 

log(35/19) = log(1.05^t)

log(35/19) = t(log 1.05)

 

t = [log(35/19)/log(1.05)]

 

t = 12.5211

 

t = 12 1/2 years to accumulate $7000

 

For a whole number round up to 13 years

Answer 2

7000 ≤ 3800(1 + 0.05)t

7000 ≤ 3800(1.05)t

7000 ≤ 3990t

 

Can you solve for t and answer?