Word math problem

Question

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

 

Suppose that you have $4000 to invest. Which investment yields the greater return over 6 years: 6.25% compounded continuously or 6.3% compounded semiannually? 

Answer 1

r = rate, t = time, p = principal, n = number of calculations per year.

 

For the continuous compounding:

 

A = 4000e^0.0625·6

A = 4000e^0.375

A = 4000 (1.45499)

A = 5819.96

 

For the semi-annual

 

A = 4000[(1 + 0.063/2)]^2·6

A = 4000[1 + 0.0315]¹²

A = 4000[1.0315]¹²

A = 4000 · 1.4508

A = 5803.51

 

The continuous calculation gains more interest.