Question

QUICK PLS Your friend is able to invest $120 a month in a 401(k) with a predicted growth rate of 3%. Your friend's company will match 50% of your friend's contributions.
PLEASE ANSWER ALL QUESTIONS

Answer 1

• The contribution of the friend's company is of: $60.

• The account's balance after 20 years will be of: $130,694.36.

• The total deposits after 20 years are given as follows: $28,800 by the friend and $14,400 by the company.

• The interest earned during this entire period was of: $87,494.36.

How to obtain the balance?

The balance is obtained using the future value formula, which is presented as follows:

$B = \frac{P\left(\left(1 + \frac{r}{n}\right)^{nt}-1\right)}{\frac{r}{n}}$

The meaning of each parameter is explained as follows:

• P is the total month deposit.

• r is the interest rate.

• n is the number of coupoundings per period, that is, compoundings per year.

• t is the number of years.

The deposits will be of:

• Friend: $120.

• Company: $60, as it is half of the friend.

Then the parameter P is of:

P = 120 + 60 = 180.

The remaining parameters to obtain the balance after 20 years are given as follows:

r = 0.03, n = 12, t = 20.

Then the balance after 20 years is obtained as follows:

$B = \frac{P\left(\left(1 + \frac{r}{n}\right)^{nt}-1\right)}{\frac{r}{n}}$

$B = \frac{180\left(\left(1 + \frac{0.03}{12}\right)^{12 \times 20}-1\right)}{\frac{0.03}{12}}$

B = $130,694.36.

The total deposits will be of:

• Friend: 120 x 20 x 12 = $28,800.

• Company: half of friend -> $14,400.

The interest accrued is the balance subtracted by the total deposits, hence:

130694.36 - (28800 + 14400) = $87,494.36.

A similar problem, also featuring the future value formula, is presented at brainly.com/question/24703884

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