9514 1404 393
Answer:
10.7 years
Step-by-step explanation:
The formula for the balance in an account earning compound interest is ...
A = P(1 +r/n)^(nt)
where principal P is invested at annual rate r compounded n times per year for t years. We want to solve for t.
5800 = 3500(1 +0.0475/4)^(4t)
58/35 = 1.011875^(4t) . . . divide by 3500 and simplify a bit
log(58/35) = 4t·log(1.011875) . . . . take logs
t = log(58/35)/(4·log(1.011875)) . . . . divide by the coefficient of t
t ≈ 10.6966 ≈ 10.7
The person must leave the money n the bank for about 10.7 years for it to reach $5800.
