Final answer:
To determine the future value of Richard's 401(k) after 30 years with monthly deposits of $247 and an annual interest rate of 3.6%, we use the future value of an annuity formula. Plugging in the values, we calculate the amount that Richard's 401(k) will accrue over the 30-year period, rounding to the nearest cent.
Step-by-step explanation:
Richard has enrolled in a 401(k) saving plan and intends to deposit $247 each month. Since his employer does not contribute to his account, we need to calculate the future value of Richard's account based on his own contributions and the annual interest rate of 3.6%. We have to solve this mathematical problem completely using the formula for the future value of an annuity, which is given by:
FV = P * [(1 + r)^nt - 1] / r
where:
FV is the future value of the annuity,
P is the periodic payment amount,
r is the interest rate per period,
n is the number of periods per year, and
t is the number of years.
For Richard's 401(k), we plug in the following values:
P = $247 (monthly deposit),
r = 0.036/12 (monthly interest rate),
n = 12 (months in a year),
t = 30 (years of deposit).
So, the future value formula becomes:
FV = 247 * [(1 + (0.036/12))^(12*30) - 1] / (0.036/12)
Calculating that, we get:
FV = 247 * [(1 + 0.003)^360 - 1] / 0.003
FV = 247 * [1.003^360 - 1] / 0.003
After solving this, the future value of Richard's 401(k) will be the value we get from the calculation. Remember to round your answer to the nearest cent.