Richard is saving money for a down payment on an expensive g

Richard is saving money for a down payment on an expensive guitar. He needs $1,500 in 9 months to make his down payment and is saving money in an annuity yielding an annual interest rate of 6% compounded monthly. If the annuity requires that Richard make monthly investments, what annuity payment must Richard make to save enough for his guitar down payment?

Solution

Future Value = Periodic payment[ (1+r)^n -1]/r

r = 0.06/12 =0.005

n = 9

Future value = $1500

So, plugging all values:

1500= P[ 1.005^9 -1]/0.005

1500 = P(9.18211)

Periodic payment = 1500/9.18211 = $ 163.36