Question

Suppose you invest $50 a month in an annuity that earns 4% APR compounded monthly. How much money will you have in this account after 3 years?

Answer 1

Answer:1909.08

Explanation:

Answer 2

To solve this we are going to use formula for the future value of an ordinary annuity:
`FV=P[ ((1+ (r)/(n) )^(nt) -1)/( (r)/(n) ) ]`
where

`FV` is the future value

`P` is the periodic payment

`r` is the interest rate in decimal form

`n` is the number of times the interest is compounded per year

`t` is the number of years

We know from our problem that the periodic payment is $50 and the number of years is 3, so
`P=50` and
`t=3`. To convert the interest rate to decimal form, we are going to divide the rate by 100%

`r= (4)/(100)`

`r=0.04`
Since the interest is compounded monthly, it is compounded 12 times per year; therefore,
`n=12`.
Lets replace the values in our formula:

`FV=P[ ((1+ (r)/(n) )^(nt) -1)/( (r)/(n) ) ]`

`FV=50[ ((1+ (0.04)/(12) )^((12)(3)) -1)/( (0.04)/(12) ) ]`

`FV=1909.08`

We can conclude that after 3 years you will have $1909.08 in your account.