Question

Use the compound interest formulas A = Pert and A = P(1+r/n)^nt to solve.

Suppose that you have $11,000 to invest. Which investment yields the greater return over 10 years: 6.25% compounded continuously or 6.3% compounded semiannually? Show your work

Answer 1

Well for your compounded continuously option, we just plug in the numbers into the A =Pe^(rt) formula. P is your principal, your initial amount, so 11,000. Rate is your percentage written as a decimal, so .0625 and time is 10. This gives us this equation:
A=11000e(10)(.0625)
For the second equation, r is again written as a decimal, but is .063 this time. Time is still 10 years. N is the amount of times the interest is compounded each year. So semi-annually means twice a year, meaning n = 2. So if we plug the numbers into that formula, we get:
A=11000(1+.0632)(2)(10)
Now you just need to do the calculator work and see which yields the greater return :3

Answer 2

So you understand?