Grandparents contribute into an account at the beginning of each month an investment that pays 8%, compounded monthly, they want the balance to be $150,000 at the end of 18 years.

Question

(a) State whether the problem relates to an ordinary annuity or an annuity due. 

(b) Solve the problem. (Round your answer to the nearest cent.) 

Answer 1

FV = 150,000

n = 18 x 12 = 216

r = .08 / 12 = 0.0066667

Solve for PMT using the formula or using Excel.

PMT = 310.37

Answer 2

(A) is simple. It is an annuit due because payments take place at the beginning of the period.

(B) To get the answer you need the formula for the future value of an annuity and then you need to work backwards. In this instance it is

FV=PMT*(1+r)*(1+r)ⁿ-1/r

You then need to know what your terms are.

FV=$150,000

r=8%/12=0.667%

N=18*12=216

PMT=?

Now you just rewrite the formula and substitute in the variables to get the answer.