How long would it take for Nico to save an adequate amount for retirement if he deposits $40,000 per year into an account beginning one year from today that pays 12 percent per year if he wishes to have a total of $1,000,000 at retirement?

Answer: It will take Nico approximately 12 years

Explanation:

Payments = $40000

r = 12%

Future Value = 1000 000

Future Value annuity = Payments ((1 + r) ^n - 1) / r

1000000 = 40000 ((1 + 0.12) ^n - 1) / 0.12

40000 ((1.12) ^n - 1) = 1000000 x 0.12

(1.12) ^n - 1 = 120000/40000

(1.12) ^n = 3 + 1

nlog (1.12) = log (4)

n = log (1.12) / log (4) = 12.232510748

n ≈ 12 years

It will take Nico approximately 12 years

12.29 years

Explanation:

to determine the number of years (n) we can use the future value formula for an annuity:

future value of an annuity = payment x [ (1 + r) ⁿ - 1] / r

r = 12% payment = 40,000 future value = 1,000,000

1,000,000 = 40,000 x [ (1 + 12%) ⁿ - 1] / 12% = 40,000 x (1.12ⁿ - 1) / 12%

(1.12ⁿ - 1) = 1,000,000 x 12% / 40,000

(1.12ⁿ - 1) = 3

1.12ⁿ = 3 + 1 = 4

nlog1.12 = log4

n = log4 / log1.12 = 0.602 / 0.049 = 12.29 years