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

Option B.

Explanation:

The future value formula, for an annuity, is:

`FV = (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 = (0.02)/(12) = 0.00167`

Find the final amount of the account.

`FV = (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.