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How much must be deposited today into the following account in order to have $50,000 in 7 years for a down payment on a house? Assume no additional deposits are mad An account with monthly compounding and an APR of 6% $ ◻ should be deposited today. (Do not round until the final answer. Then round to the nearest cent as needed.)

How much must be deposited today into the following account in order to have $50,000\$50,000 in 77 years for a down payment on a house? Assume no additional deposits are made. An account with monthly compounding and an APR of 6%6\% $\$ □\square should be deposited today. (Do not round until the final answer. Then round to the nearest cent as needed.)

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Full solution

Q. How much must be deposited today into the following account in order to have $50,000\$50,000 in 77 years for a down payment on a house? Assume no additional deposits are made. An account with monthly compounding and an APR of 6%6\% $\$ □\square should be deposited today. (Do not round until the final answer. Then round to the nearest cent as needed.)
  1. Calculate Future Value: Calculate the future value using the formula for compound interest: FV=PV(1+rn)(nt)FV = PV(1 + \frac{r}{n})^{(nt)}. Here, FV=$50,000FV = \$50,000, r=0.06r = 0.06 (annual interest rate), n=12n = 12 (compounding monthly), t=7t = 7 years.
  2. Calculate Power: Calculate the power (1.005)84(1.005)^{84} using a calculator to ensure accuracy.
  3. Find Present Value: Divide the future value by the result from the previous step to find the present value.

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