New Car Savings

Jingjie wants to buy a new mini-van (cool!) to replace her aging SUV. She estimates that her current SUV will last three more years and have no salvage (trade-in) value. She will purchase the new van after the SUV wears out (in three years). The type of van she would like to buy currently costs $25,000. Jingjie estimates that the price of the van will grow at 2% per year (compounded yearly) for the next three years.

When she buys the van three years from now, she will finance the purchase with a down payment and a five-year loan (60 month) from her bank. Jingjie expects the bank to charge her 6% interest per year compounded monthly. Once she buys the car, Jingjie wants her monthly payment to be $300 per month.

Jingjie currently does not have any savings. However, she can deposit money each month (including the last month) into a savings account that earns 3% per year, compounded monthly. How much does Jingjie need to save each month to ensure that she has enough money for a down payment, such that her car payment will be $300/month?