Question 299974
A college loan of $44,000 is made at 3% interest, compounded annually. After t years, the amount due, A, is given by the function.
A(t) = 44,000 (1.03)^t.
After what amount of time will the amount reach $54,000?
.
Simply set A(t) equal to 54000 and solve for t:
{{{A(t) = 44,000 (1.03)^t}}}
{{{54000 = 44000 (1.03)^t}}}
{{{54000/44000 = 1.03^t
{{{54/44 = 1.03^t}}}
{{{log(1.03,(54/44)) = t}}}
{{{log(54/44)/log(1.03)) = t}}}
{{{ 6.93 = t }}}
Rather:
t = 6.93 years