Questions: Use the savings plan formula to answer the following question. Your goal is to create a college fund for your child. Suppose you find a fund that offers an APR of 4%. How much should you deposit monthly to accumulate 87,000 in 16 years? You should invest each month. (Do not round until the final answer. Then round to two decimal places as needed.)

Use the savings plan formula to answer the following question. Your goal is to create a college fund for your child. Suppose you find a fund that offers an APR of 4%. How much should you deposit monthly to accumulate 87,000 in 16 years? You should invest each month. (Do not round until the final answer. Then round to two decimal places as needed.)
Transcript text: possible Use the savings plan formula to answer the following question. Your goal is to create a college fund for your child. Suppose you find a fund that offers an APR of 4\%. How much should you deposit monthly to accumulate \$87,000 in 16 years? You should invest \$ $\square$ each month. (Do not round until the final answer. Then round to two decimal places as needed.)
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Solution

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Solution Steps

Step 1: Convert the Annual Percentage Rate (APR) to a monthly interest rate

The APR is given as 4%. To convert this to a monthly interest rate, we divide by 12 and convert it to decimal form: \[ r = \frac{APR}{12} = \frac{4}{12} = 0.00333 \]

Step 2: Calculate the total number of deposits

Since the deposits are made monthly over a period of 16 years, the total number of deposits (n) is: \[ n = T \times 12 = 16 \times 12 = 192 \]

Step 3: Use the rearranged future value of an annuity formula to calculate the monthly deposit amount

The formula to calculate the monthly deposit amount (P) is given by rearranging the future value of an annuity formula: \[ P = \frac{FV}{\left( \frac{(1 + r)^n - 1}{r} \right)} \] Substituting the values of FV = 87000, r = 0.00333, and n = 192 into the formula, we get: \[ P = \frac{87000}{\left( \frac{(1 + 0.00333)^192 - 1}{0.00333} \right)} = 324.22 \]

Final Answer:

The monthly deposit amount required to accumulate a future value of 87000 in 16 years with an APR of 4% is approximately 324.22.

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