Tasha invests $5,000 annually at 6% and $5,000 annually at 8%. Thomas invests $10,000 annually at 7%. Which statement accurately compares the two investments if interest is compounded annually?

I do not see the statements

.5*(1.06)^n + .5(1.08)^n
compared to
1 * (1.07)^n

well, look after a year

.5*1.06 + .5*1.08 = 1.07

1 * 1.07 = 1.07

look after 5 years
.5(1.06)^5 + .5(1.08)^5 = 1.403776827
1.07^5 =1.402551731 less

look after 20 years
.5*1.06^20 + .5*1.08^20 = 3.9340463
1.07^20 = 3.869684462 less
Tasha wins because the 8% half makes the Tasha investment grow faster

To compare the two investments, we need to calculate the future value of each investment after a certain number of years.

For Tasha's investment, she invests $5,000 annually at 6% and $5,000 annually at 8%. Since both investments are compounded annually, we can calculate the future value using the formula:

FV = P(1 + r)^n

Where FV is the future value, P is the principal amount, r is the annual interest rate as a decimal, and n is the number of years.

For the first investment, Tasha invests $5,000 annually at 6% for a certain number of years. Let's assume she invests for 10 years. The future value of this investment can be calculated as:

FV1 = $5,000(1 + 0.06)^10

For the second investment, Tasha invests $5,000 annually at 8% for the same number of years. The future value of this investment can be calculated as:

FV2 = $5,000(1 + 0.08)^10

Now let's calculate the future value of Thomas' investment. He invests $10,000 annually at 7% for the same number of years (10 years). The future value of his investment can be calculated as:

FV3 = $10,000(1 + 0.07)^10

After calculating these values, we can compare the future values of the two investments. The statement that accurately compares the two investments is the one that states the highest future value among the three calculations.

Each person will have exactly the same amount over time because each invested $10,000 at an average interest rate of 7%.

Tasha’s investment will yield more over many years because the amount invested at 8% causes the overall total to increase faster.

Thomas’s investment will yield more from the start because he has more money invested at the average percentage rate.

Tasha’s investment will be greater at first because she invested some at a higher rate, but Thomas’s investment will be greater over the long run.