Question

 Lisa Simpson wants to have ​$1,200,000 in 40 years by making equal annual​ end-of-the-year deposits into a​ tax-deferred account paying 8.75 percent annually. What must​ Lisa's annual deposit​ be?

Answer 1

since Lisa simpson wants to make equal annual end of the year deposits, it can be said that she wants to make end of year annuity payments.

since she wants to have $1,200,000 in 40 years.

it can be said that the future value of annuity is $1,200,000.

The annual payments to be made can be known using, future value of annuity formula.

future value of annuity = P[(1+r)^n-1]/r

here,

future value of annuity = 1,200,000

P is the annual payment to be found out.

r =8.75%

=>0.0875.

n=40

=>1,200,000 = P*[(1.0875)^40 -1]/0.0875

=>1,200,000 = P*[28.6530347-1]/0.0875

=>1,200,000 = P*[27.6530347]/0.0875

=>1,200,000 = P*316.034682

=>P = 1,200,000 / 316.034682

=>$3,797.05.

Lisa's annual deposit will be $3,797.05.