part 1 $60,000 invested at 5% compounded semiannually
the formula for this calculation is
Future value = Present value x (1 + r/n)ny
where r = rate as a decimal, n = number of compounding periods per year, and y = number of years
FV = $60,000 x (1 + 0.05/2)2•4 which becomes $60,000 x 1.0258
FV ≅ $73,104
part 2 $60,000 invested for 4 years at 4.75% compounded continuously
the formula for this calculation
Future value = Present value • ery
where e = Euler's number (2.71828), r = rate as a decimal, and y = years
FV = $60,0000•(2.71828.0475•4) = $60,000 • 2.718280.19≅ $72,554
part a the plan using 5% will earn more interest than the 4.75% plan
part b difference = (73104 - 60000) - (72554 - 60000) ≅ $550