Question

Low-risk investors should assume an interest rate of 6% annually. Moderate-risk investors should use 8%, high-risk investors should assume 10%, and ultra high-risk investors should use 12%. For purposes of this calculation, ignore any Social Security benefit received. Assume you are 22 years old and want to have a $1,600,000 at retirement (age 70). How much do you need to save each quarter to reach your goal if you are a low-risk investor?

Answer 1

Future value of annuity = P * [(1 + r)ⁿ - 1] / r

where P = periodic payment. We need to calculate this.

r = periodic rate of interest. This is 6%/4 = 1.5%. We divide by 4 since we need to convert the annual rate into quarterly rate)

n = number of periods. This is 48 * 4 = 192 (there are 48 years, or 192 quarters in the years from age 22 to age 70)

$1,600,000 = P * [(1 + 1.5%)¹⁹² - 1] / 1.5%

P = ($1,600,000 * 1.5%) / [(1 + 1.5%)¹⁹² - 1]

P = $1,460.09

You need to save $1,460.09 each quarter to reach your goal