Question

Zheng sen wishes to accumulate​ $1 million by the end of 20 years by making equal annual endminus−ofminus−year deposits over the next 20 years. if zheng sen can earn 10 percent on his​ investments, how much must he deposit at the end of each​ year?

Answer 1

$17,459.62  
The equation for the value of an investment with periodic contributions is:
 B = P(1+r)^y + c(((1+r)^y -1)/r)
 where
 B = Balance
 P = Initial principle
 r = interest rate
 c = periodic contribution
 y = number of years.
 
 For this problem, the initial principle is 0, so we have a simplified equation of:
 B = c(((1+r)^y -1)/r)
 
 Let's solve for c, substitute the known values, and calculate
 B = c(((1+r)^y -1)/r)
 B/(((1+r)^y -1)/r) = c
 1000000/(((1+0.10)^20 -1)/0.10) = c
 1000000/(((1.10)^20 -1)/0.10) = c
 1000000/((6.727499949 -1)/0.10) = c
 1000000/(5.727499949/0.10) = c
 1000000/57.27499949 = c
 17459.62477 = c 
 So Zheng needs to contribute $17,459.62 at the end of every year.