#of years of a loan?

Question

Ty borrowed $6800 at 3.4%/a compounded semi-annually. He knows he will pay $7781.74 for the principal and interest at the end of the loan, but he cannot remember the length of the loan. How many years is Ty’s loan?

Answer 1

7781.84 = 6800(1 + .034/2)^2t

7781.84/6800 = (1 + .034/2)^2t

ln(7781.84/6800) = 2tln(1 + .034/2)

t = ln(7781.84/6800)/2ln(1 + 0.34/2)

t = 4 years