Question

$765.13 is deposited at the end of each month for 3 years in an account paying 2% Interest compounded monthly. Find the final amount of the account. Round to the nearest
cent
O A. $27,598.32
OB. $28,363,45
OC. $29,128.58
OD. $26,787.27

Answer 1

Answer:

Option B.

Step-by-step explanation:

The future value formula, for an annuity, is:

$FV = \frac{P((1+r)^{n} - 1)}{r}$

An annuity means that a number of payments happen during the period(an year, for example).

P is the value of the deposit, r is the interest rate, as a decimal, and n is the number of deposits.

In this question:

Deposits of $765.13, so $P = 765.13$

Each month, for 3 years. An year has twelve months, so $n = 3*12 = 36$

2% Interest a year. An year has 12 months, so $r = \frac{0.02}{12} = 0.00167$

Find the final amount of the account.

$FV = \frac{765.13*((1 + 0.00167)^{36} - 1)}{0.00167} = 28,363.46$

The final amount of the account will be $28,363.46, which is option B.