Your goal is to create a college fund for your child. Suppose you find a fund that offers an APR of 5% . How much should you deposit monthly to accumulate $90000 in 16 years? Question content area bottom Part 1 You should invest $ enter your response here each month. (Do not round until the final answer. Then round to two decimal places as needed.)
1 - Will consider 5% APR as "compounded monthly".
2 - Use this formula to find the monthly payments.
3 - FV=90,000; R=0.05/12; N=16*12;PMT = FV*(((1 + R)^N - 1)^-1* R)
4 - PMT =$ 306.91 - monthly payments that must be made for 16 years or: 16 x 12==192 months.
Hey there! Calculating the monthly deposit required to accumulate $90,000 in 16 years with an APR of 5% is an important step towards building a college fund for your child.
To determine the monthly deposit, we can use the formula for the future value of an ordinary annuity:
FV = P * [(1 + r)^n - 1] / r
Where: FV is the future value ($90,000), P is the monthly deposit, r is the monthly interest rate (APR divided by 12), and n is the total number of months (16 years multiplied by 12 months).
Plugging in the values, we have:
$90,000 = P * [(1 + 0.05/12)^(16*12) - 1] / (0.05/12)
To solve for P, we can rearrange the equation:
P = ($90,000 * (0.05/12)) / [(1 + 0.05/12)^(16*12) - 1]
Performing the calculations, the monthly deposit required to accumulate $90,000 in 16 years at an APR of 5% is approximately $321.35.
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