Question

Tim has a savings account with the bank. The bank pays him 1% per year. He has $6,400 and wonders when it will reach $6,900. When will his savings reach $6,900? If necessary, round your answer to the nearest whole number.
Considering interest is calculated yearly, it will take Tim approximately ____ year(s).

Answer 1

Answer:

8 years

Step-by-step explanation:

Tim's account balance has an initial value of $6400 and is multiplied yearly by the factor 1.01. Thus, it can be described by the exponential equation ...

b = 6400·1.01^t

where b is the balance after t years.

Putting in the desired balance, we can find t.

6900 = 6400·1.01^t

1.078125 = 1.01^t . . . . . divide by 6400

log(1.078125) = t·log(1.01) . . . . take the logarithm of both sides

log(1.078125)/log(1.01) = t ≈ 7.56 ≈ 8 . . . . . divide by the coefficient of t

It will take Tim approximately 8 years to reach a balance of $6900.

_____

The problem can also be solved using a graphing calculator.