Question

A person invested $210 in an account growing at a rate allowing the money to double every 10 years. how long, to the nearest tenth of a year would it take for the value of the account to reach $1,510?

Answer 1

28.5 years

Explanation:

You want to know how many years it takes for a $210 investment to have a value of $1510 if it doubles in value every 10 years.

Doubling

When an account doubles in value in 10 years, its value after t years is given by ...

A = P(2^(t/10))

We have A=1510, P=210, and we want to find t.

Solution

1510 = 210(2^(t/10)) . . . . . . use the given values

1510/210 = 2^(t/10) . . . . . divide by 210

Taking logarithms gives ...

log(1510/210) = (t/10)log(2)

Dividing by the coefficient of t, we have ...

t = 10·log(1510/210)/log(2) ≈ 28.46

It would take about 28.5 years for the value of the account to reach $1510.