Question

QuestRecently, More Money 4U offered an annuity that pays 6.6% compounded monthly. If $1,504 is deposited into this annuity every month, how much is in the account after 11 years? How much of this is interest?Type the amount in the account: $(Round to the nearest dollar.)

Answer 1

Amount = $3102.75

Interest = $1598.75

Step-by-step explanation

The annuity pays 6.6% compounded monthly.

The formula for an Amount compounded at a rate of r after t years is given as:

`A\text{ = P(1 + }(r)/(n))^(nt)`

where P = principal (amount deposited) = $1,504

r = rate = 6.6% = 0.066

n = 12 (12 months in a year)

t = number of years = 11 years

Therefore, the amount in the account after 11 years is:

`A\text{ = 1504(1 +}(0.066)/(12))^{12\cdot\text{ 11}}`
`\begin{gathered} A=1504(1+0.0055)^(132) \\ A\text{ = 1504(}1.0055)^(132) \\ A\text{ = 1504 }\cdot\text{ 2.063} \\ A\text{ = \$3102.75} \end{gathered}`

That's the amount in the account after 11 years.

This means that the amount of interest after 11 years is the amount after 11 years minus the amount that was there initially:

Interest = 3102.75 - 1504

Interest = $1598.75