Final answer:
To have $10,000 in ten years in an account with 10% annual compound interest, you need to deposit approximately $3,855.43 today.
Step-by-step explanation:
To find out how much money you need to put into a bank account that pays 10% interest compounded annually to have $10,000 in ten years, you can use the future value formula for compound interest:Present Value = Future Value / (1 + interest rate)timeHere, the Future Value (FV) is $10,000, the interest rate (r) is 10% or 0.10, and the time (t) is 10 years.Plugging these values into the formula gives us: Present Value = $10,000 / (1 + 0.10)10Present Value = $10,000 / (1.10)10Present Value = $10,000 / 2.5937 Present Value ≈ $3,855.43 You would need to deposit approximately $3,855.43 today in a bank account with 10% annual compound interest to have $10,000 in ten years.
To find the future value (FV), present value (PV), annual interest rate, and time period, we can use the formula for compound interest: FV = PV × e^(rt), where PV is the initial investment, r is the interest rate, t is the time period, and e is the base of the natural logarithm. In this case, we have PV, r, and t, and we need to find FV.a) To find the future value, we can substitute the given values into the formula: FV = PV × e^(rt) = PV × e^(0.08 × 10) = PV × e^0.8b) To find the present value, we need to rearrange the formula: PV = FV / e^(rt).c) To find the annual interest rate, we need to rearrange the formula: r = ln(FV / PV) / t.d) To find the time period, we need to rearrange the formula: t = ln(FV / PV) / r.