Questions: At the time of her grandson's birth, a grandmother deposits 7000 in an account that pays 6.5% compounded monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawals are made during this period? The value of the account will be (Round to the nearest dollar as needed.)

At the time of her grandson's birth, a grandmother deposits 7000 in an account that pays 6.5% compounded monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawals are made during this period? The value of the account will be (Round to the nearest dollar as needed.)
Transcript text: N Help ATICS -2024FA-FA-MATH-1332-03-WC Emma Upchurch 11/04/24 7:04 PM Review Question 36, 8.4.37 HW Score: 84.21\%, 32 of 38 points Points: 0 of 1 Save At the time of her grandson's birth, a grandmother deposits $\$ 7000$ in an account that pays $6.5 \%$ compounded monthly. What will be the yalue of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawals are made during this period? B Click the icon to view some finance formulas. The value of the account will be \$ $\square$ (Round to the nearest dollar as needed.) View an example Get more help - Clear all Check answer Start
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Solution

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Solution Steps

Step 1: Convert the annual nominal interest rate from a percentage to a decimal

The annual nominal interest rate in decimal is 0.065.

Step 2: Identify the number of times the interest is compounded per year

The interest is compounded 12 times per year.

Step 3: Determine the total number of compounding periods

The total number of compounding periods is 252.

Step 4: Use the future value formula to calculate the future value of the investment

Using the formula \(FV = P(1 + \frac{r}{n})^{nt}\), the future value of the investment is calculated. Substituting the values, we get \(FV = 7000(1 + \frac{0.065}{12})^{252}\).

Step 5: Round the result to the nearest dollar as needed

The future value of the investment, rounded to 0 decimal places, is $27309.

Final Answer:

The future value of the investment is approximately $27309.

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