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?

Question

Business

Justin Wiggins

25 February, 18:10

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?

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Answers (1)

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Vanessa Parsons · Answer 1

The smallest Q that will suffice is 409.86

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