Question

A college loan of $28,000 is made at 8% interest, compound annually. After t years, the amount due, A is given by the function A (t) =28,000 (1.08^t)
a) After what amount of the time will the amount due reach $42,000?
t=_____ years
Round to the nearest whole number.

Answer 1

t=a/p

Answer 2

\[42000 = 28000(1.08^t)\]

\[42000/28000 = 1.08^t\]

3/2 = 1.08^t

take the log of both sides... e or base 10

\[\ln(\frac{3}{2}) = t \times \ln(1.08)\]

\[t = \frac{\ln(\frac{3}{2})}{\ln(1.08)}\]

solve for t

Answer 3

Answer is 5