Annuities on deposit at the end of each month

Question

Formula: P=A(r/n)/ [(1+r/n)^nt -1]

How much should you deposit at the end of each month into an investment account that pays 5.5% compounded monthly to have $3 million when you retire in 41 years? How much of the $3 million comes from interest? In order to have $3 million in 41 years, you should deposit $______ each month.

Answer 1

The formula is given.

P =?

A=3,000,000

t = 41 years,

n=12,

r =0.055 =5.5%

P=3,000,000 (0.055/12)/[(1+.055/12)^12•41-1]

P=3,000,000(0.0045833)/1.0045833⁴⁹¹

P=1456.12

 

Your monthly payment will be $1456.12.

You will make principle payment of

Principle = n•t•monthly payment

             = 12•41•1456.12

             = $716,411.04

Interest earned

A-Principle = 3,000,000-716,411.04=2,283,588.96