Final answer:
The amount to be invested now to accumulate $12,700 at 5% compound interest annually over 11 years is $7,796.70, which corresponds to option A). The compound interest formula P = A / (1 + r/n)nt was used to calculate this.
Step-by-step explanation:
To find the amount that should be invested now to accumulate $12,700 at 5% compounded annually for 11 years, we can use the formula for compound interest, which is A = P(1 + r/n)nt. In this formula, A is the future value we want to reach ($12,700), P is the principal amount we need to find, r is the annual interest rate (0.05 for 5%), n is the number of times interest is compounded per year (1 for annually), and t is the time in years (11).
Let's rearrange the formula to solve for P: P = A / (1 + r/n)nt. Plugging in the values, we get P = $12,700 / (1 + 0.05/1)1*11. This simplifies to P = $12,700 / (1.05)11 = $7,796.70.
Therefore, the amount that should be invested now is $7,796.70, which corresponds to option A).