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