Question

How long would it take for you to save an adequate amount for retirement if you deposit $40,000 per year into an account beginning today that pays 12 percent per year if you wish to have a total of $1,000,000 at retirement? PLEASE show how to do it on a Financial calculator.

A) 12.2 years

B) 10.5 years

C) 14.8 years

D) 11.5 years

Answer 1

Option (D) is correct

Here since the payments are made at the beginning of each year, so it is annuity due. We will use the following future value of annuity due formula:

FVAD = (1 + r) * P * ((1 + r)ⁿ - 1 / r)

where, FVAD is future value of annuity due = $1000000, P is the periodical amount = $40000, r is the rate of interest = 12% and n is the time period

Now, putting these values in the above formula, we get,

$1000000 = (1 + 12%) * $40000 * ((1 + 12%)ⁿ - 1 / 12%)

$1000000 = (1 + 0.12) * $40000 * ((1 + 0.12)ⁿ - 1 / 0.12)

$1000000 * 0.12 = (1.12) * $40000 * ((1.12)ⁿ - 1)

$120000 = $44800 * ((1.12)ⁿ -1)

$120000 / $44800 = (1.12)ⁿ -1

2.67857 = (1.12)ⁿ - 1

2.67857 + 1 = (1.12)ⁿ

(3.67857)ⁿ = (1.12)ⁿ

(1.12)^11.5 = (1.12)ⁿ

n is 11.5 years.So, it will take 11.5 years.