Question

$1334 is deposited into a savings account at 8% interest, compounded quarterly. To the nearest year, how long will it take for the account balance to reach $1,000,000?

Answer 1

Answer:

  84 years

Step-by-step explanation:

The future value of an investment is given by ...

  FV = P(1 +r/n)^(nt)

where P is the principal amount, r is the annual rate, and n is the number of times per year interest is compounded. Filling in the given values and solving for t, we get ...

  1000000 = 1334(1 +.08/4)^(4t)

  749.6252 ≈ 1.02^(4t) . . . . divide by 1334 and simplify

  log(749.6252) ≈ 4t·log(1.02) . . . . take logarithms

  t ≈ log(749.6252)/(4·log(1.02)) ≈ 83.57

It will take about 84 years for the account balance to reach $1,000,000.