Question

You just won $30,000 and deposited your winnings into an account that pays 3.9 percent interest, compounded annually. how long will you have to wait until your winnings are worth $75,000? 22.29 years 25.00 years 23.95 years 21.24 years 22.67 years

Answer 1

For this case we have an equation of the form:
 $y = A * (b) ^ x$
 Where,
 A: initial amount
 b: growth rate
 x: number of years
 Substituting values we have:
 $y = 30000 * (1,039) ^ x$
 By the time the earnings increase to 75000 we have:
 $75000 = 30000 * (1,039) ^ x$
 From here, we clear x:
 $(1,039) ^ x = (75000/30000) log1.039 ((1.039) ^ x) = log1.039 ((75000/30000))$
 $x = log1.039 ((75000/30000)) x = 23.95 years$
 Answer:
 you will have to wait until 23.95 years your winnings are worth $ 75,000