Question

# John buys a new solar power energy grid worth \$408,756 for his company's warehouse. The contract...

John buys a new solar power energy grid worth \$408,756 for his company's warehouse. The contract stipulates payments will use a nominal interest rate of 7.7% compounded monthly for 40 months. John agrees to pay \$ 27 as down payment on the condition that the first payment will not be until the start of the 8 month if he pays interest on the current balance until he begins payments.
Determine the monthly payments.

Price of the grid = \$408756

Monthly interest rate = 7.7%/12

Time for payment = 33 months

Down payment = \$27

Net amount of loan = 408756-27 = \$408729

Now, interest on loan is already paid, so starting 8th month, loan amount will remain same as \$408729. Further, the payment starts in the beginning of each month starting month-8, so it is a case of annuity due.

Let, monthly payment = P

Then,

408729 = (P*(1-1/(1+7.7%/12)^33)/(7.7%/12))*(1+7.7%/12)

(408729/(1+7.7%/12)) = (P*(1-1/(1+7.7%/12)^33)/(7.7%/12))

406123 = P*29.65488

P = \$13694.98 or \$13695

So, the monthly payment will be \$13695.