The output of the following function is the future value of an account if:PV dollars are depositedLeft for Y yearsAt an annual rate of rWith n compounds per year 𝐹𝑉=𝑃𝑉(1+𝑟𝑛)(𝑛𝑌) Philza plans to put $4,825 dollars in an account that earns 3.2% interest compounded monthly. Use the formula or the FV function in Excel to find Philza's account balance in 6 years. (Do not round until the final answer, then round your answer to the nearest dollar, and don't include the dollar sign.
Question
The output of the following function is the future value of an account if:PV dollars are depositedLeft for Y yearsAt an annual rate of rWith n compounds per year 𝐹𝑉=𝑃𝑉(1+𝑟𝑛)(𝑛𝑌) Philza plans to put $4,825 dollars in an account that earns 3.2% interest compounded monthly. Use the formula or the FV function in Excel to find Philza's account balance in 6 years. (Do not round until the final answer, then round your answer to the nearest dollar, and don't include the dollar sign.
Solution
To solve this problem, we need to plug the given values into the future value formula:
FV = PV * (1 + r/n)^(n*Y)
Where:
- PV = $4,825 (the initial deposit)
- r = 3.2% or 0.032 (the annual interest rate)
- n = 12 (the number of times interest is compounded per year, which is monthly in this case)
- Y = 6 (the number of years the money is left in the account)
Substituting these values into the formula, we get:
FV = 4825 * (1 + 0.032/12)^(12*6)
Now, we just need to calculate the expression on the right side of the equation.
First, calculate the value inside the parentheses: 1 + 0.032/12 = 1.00266666667
Next, raise this value to the power of (12*6) = 72: 1.00266666667^72 = 1.21647733142
Finally, multiply this result by the initial deposit: 4825 * 1.21647733142 = 5871.95
So, the future value of Philza's account in 6 years will be approximately $5872 when rounded to the nearest dollar.
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