Question

You plan to "go green" and install solar panels on your home in 36 months.
The solar company has a payment plan whereby you will pay for the panels in 120 monthly payments (installments) starting in month 37
Each monthly installment will be for $200 per month.
How much would you have to invest each month (the same amount in each month), starting in one month, for 35 months , to exactly pay for the solar panels ,if your investments earn 3.00% APR (compounded monthly)?

Answer 1

Future Value of Investments at Month 36=monthly investment/(r/12)*((1+r/12)^35-1)*(1+r/12)
Present Value of Payments at Month 36=monthly payment/(r/12)*(1-1/(1+r/12)^120)
Future Value of Investments at Month 36=Present Value of Payments at Month 36
Let the amount invested each month be x
Hence,
x/(3%/12)*((1+3%/12)^35-1)*(1+3%/12)=200/(3%/12)*(1-1/(1+3%/12)^120)
=>x=565.59