- To find the future value in year 9 of a $2,000 deposit in year 1 and another $1,500 deposit at the end of year 3 using a 10 percent interest rate, you need to first find the future value of the $2,000 deposit after 9 years. To do this, you can use the formula FV = PV * (1 + r)^t, where FV is the future value, PV is the present value (in this case, $2,000), r is the interest rate (in this case, 10 percent), and t is the number of years (in this case, 9). Plugging in these values, you get FV = $2,000 * (1 + 0.1)^9 = $2,000 * 2.59374 = $5,187.48. Next, you need to find the future value of the $1,500 deposit at the end of year 3. To do this, you can use the same formula, but now t is 6 (since it is 6 years from the end of year 3 to the end of year 9). Plugging in these values, you get FV = $1,500 * (1 + 0.1)^6 = $1,500 * 1.83929 = $2,759.39. To find the total future value in year 9, you can add the future value of the two deposits together: $5,187.48 + $2,759.39 = $7,946.87.
- To find the future value of a $900 annuity payment over five years if interest rates are 8 percent, you can use the formula FV = A * [(1 + r)^t – 1] / r, where FV is the future value, A is the annuity payment (in this case, $900), r is the interest rate (in this case, 8 percent), and t is the number of years (in this case, 5). Plugging in these values, you get FV = $900 * [(1 + 0.08)^5 – 1] / 0.08 = $900 * [1.44697 – 1] / 0.08 = $900 * 0.44697 / 0.08 = $900 * 5.5871 = $5,028.39.
- To find the present value of a $2,000 deposit in year 1 and another $1,500 deposit at the end of year 3 if interest rates are 10 percent, you need to first find the present value of the $2,000 deposit. To do this, you can use the formula PV = FV / (1 + r)^t, where PV is the present value, FV is the future value (in this case, $2,000), r is the interest rate (in this case, 10 percent), and t is the number of years (in this case, 3). Plugging in these values, you get PV = $2,000 / (1 + 0.1)^3 = $2,000 / 1.331 = $1,502.27. Next, you need to find the present value of the $1,500 deposit at the end of year 3. To do this, you can use the same formula, but now t is 6 (since it is 6 years from the end of year 3 to the end of year 9). Plugging in these values, you get PV = $1,500 / (1 + 0.1)^6 = $1,500 / 1.83929 = $813.73.
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