Question

Emily purchased a bond value at $20,000 for highway construction for $8410. If the bond pays 6.8% annual interest, compounded monthly, how long must she hold it until it reaches its full face value?

Answer 1

To find out how long Emily must hold the bond until it reaches its full face value, we can use the formula for compound interest. By solving the equation, we find that Emily must hold the bond for approximately 2.87 years.

Step-by-step explanation:

To solve this problem, we need to use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (initial investment), r is the annual interest rate in decimal form, n is the number of times the interest is compounded per year, and t is the number of years.

Given that Emily purchased the bond for $8410 and its full face value is $20,000, we can set up the following equation:

20000 = 8410(1 + 0.068/12)^(12t)

To solve for t, we can use logarithms to isolate the variable:

t = log(1 + 0.068/12)((20000/8410))/log(1 + 0.068/12)(1 + 0.068/12)

Using a calculator, we find that t is approximately 34.35 months, which is equivalent to around 2.87 years.