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# math work

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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.)

Jul 2, 2023

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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.

Jul 2, 2023
#2
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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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Jul 4, 2023