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?

A = Pe^rt

P = 11,000; r = 6.25%; t = 10; e = 2.7183 approximate

A = 11,000 e ^ (0.0625 * 10)

A = 11,000 e ^0.625

A = 11,000 * 2.7183^0.625

A = 11,000 * 1.868

A = 20,548

A = P (1 + r/n) ^nt

P = 11,000; r = 6.3%; n = 2; t = 10

A = 11,000 (1 + 0.063/2) ^2*10

A = 11,000 (1 + 0.0315) ^20

A = 11,000 (1.0315) ^20

A = 11,000 (1.859)

A = 20,449

$11,000 invested at 6.25% compounded continuously over 10 years yields the greater return.