If Naomi decides that she will invest $3,000 per year in a 6% annuity for the first ten years, $6,000 for the next ten years, and $9,000 for the next ten years, how much will she accumulate? Treat each ten year period as a separate annuity. After ten years of an annuity, then it will continue to grow at compound interest for the remaining years of the 30 years.
amount
= 3000(1.06^10 - 1)/.06(1.06)^20 + 6000(1.06^10 - 1)/.06(1.06)^10 + 9000(1.06^10 - 1)/.06
= 387073.72
another way:
amount = 3000(1.06^30 - 1)/.06 + 3000(1.06^20 - 1)/.06 + 3000(1.06^10 - 1)/.06
= 387073.72
Thank you sooooo much Reiny you are a blessing tonight.
himb uhihjuhou
To determine how much Naomi will accumulate, we will calculate the accumulated value for each ten-year period separately and then sum them up.
For the first ten-year period, Naomi invests $3,000 per year in a 6% annuity. The formula to calculate the accumulated value of an annuity is:
A = P * [(1 + r)^n - 1] / r
Where:
A = Accumulated value
P = Payment per period
r = Interest rate per period
n = Number of periods
In this case, P = $3,000, r = 6% = 0.06, and n = 10. Plugging these values into the formula, we have:
A1 = 3,000 * [(1 + 0.06)^10 - 1] / 0.06
Calculating this with a calculator, A1 equals approximately $38,723.24.
For the second ten-year period, Naomi invests $6,000 per year at the same 6% interest rate. Again, using the same formula with P = $6,000, r = 0.06, and n = 10, we get:
A2 = 6,000 * [(1 + 0.06)^10 - 1] / 0.06
Calculating this, A2 equals approximately $77,446.48.
For the final ten-year period, Naomi invests $9,000 per year at the same 6% interest rate. Using the formula with P = $9,000, r = 0.06, and n = 10, we get:
A3 = 9,000 * [(1 + 0.06)^10 - 1] / 0.06
Calculating this, A3 equals approximately $116,169.72.
Finally, to find the total accumulated value, we add up the three amounts:
Total accumulated value = A1 + A2 + A3
= $38,723.24 + $77,446.48 + $116,169.72
= $232,339.44
Therefore, after thirty years of investing in different annuities, Naomi will accumulate approximately $232,339.44.