Story problem

Question

An employee wants to invent $60,000 in a pension plan. One investment offers 5% compounded semiannually. Another offers 4.75% compounded conyinuously.

a) Which investment will earn more interest in 4 yr?

b) How much more will the better plan earn?

Answer 1

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 • e^ry

where e = Euler's number (2.71828), r = rate as a decimal, and y = years

FV = $60,0000•(2.71828^.0475•4) = $60,000 • 2.71828^0.19≅ $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