Question

Stuart wishes to have $14,000 to buy a used car three years from now. He plans to accomplish this, through an account with a nominal interest rate of 3% compounded monthly, by depositing $300 at the end of each month during the first year, and Q at the end of each month during the second two years. What is the smallest Q that will suffice?

Answer 1

The smallest Q that will suffice is 409.86

Step-by-step explanation:

Since Future value of payments = 14000

300*[(1 + 3%/12)^12 - 1]/3%/12*(1 + 3%/12)^24 + Q*[(1 + 3%/12)^24 - 1]/3%/12 = 14000

Q*[(1 + 3%/12)^24 - 1]/3%/12 = 14000 - 300*[(1 + 3%/12)^12 - 1]/3%/12*(1 + 3%/12)^24

Q = 409.86

Therefore, The smallest Q that will suffice is 409.86