$4.$ GasCo wants to upgrade some capital equipment that costs $$220,000$ today. The firm would like to pay for the equipment using a payment today of $$130,000$ combined with quarterly payments for a total of $4$ years. It would like to start with a first payment and then increase payments by $2\%$ each quarter. If the interest rate is $1\%$ per quarter compounded quarterly,

calculate the amount of the first payment.