Question

You plan to "go green" and install solar panels on your home in 36 months. The...

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)?

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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

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