Question

Your grandfather made an investment of $4,000 the day you were born, as such starting to earn returns immediately. His assumption is that by investing in the average market, the investment account will earn an annual rate of 6%, which is a historical average. He will continue to make 18 more annual $1,500 deposits into this account for you, assuming you will earn the average 6% every year. Based on the above assumptions, what will be the balance of this account after the initial investment and the 18 annual returns earning the hypothetical 6%?

Answer 1

`Acumulated value=57,775.84`

Step-by-step explanation:

this problem can be solved applying the concept of annuity, keep in mind that an annuity is a formula which allows you to calculate the future value of future payments affected by an interest rate.by definition the future value of an annuity is given by:

`s_(n) =P*((1+i)^(n)-1 )/(i)`

where
`s_(n)` is the future value of the annuity,
`i` is the interest rate for every period payment, n is the number of payments, and P is the regular amount paid

But there is an special thing to keep in mind and is the initial payment so we must to calculate the 4,000 in the future so we have:

`Acumulated value=s_(n) +P*(1+i)^(n)`

`Acumulated value=1,500*s_(18) +4,000*(1+0.06)^(18)`

`Acumulated value=57,775.84`