An employee wants to invest $50,000 in a pension plan. One investment offers 6% compounded quarterly. Another offers 5.75% compounded continuously.

Question

An employee wants to invest $50,000 in a pension plan. One investment offers 6% compounded quarterly. Another offers 5.75% compounded continuously.

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

(b) How much will the better plan earn?

 

Answer 1

Compound interest:  A = p(1+r/n)^nt

A = future amount

p = principle investment = 50000

r = interest rate = .06

n = # times compounded yearly = 4

t = time in years

 

A = 50000(1+.06/4)⁴⁽⁴⁾

= $63,449.28

 

Continuous interest: A=pe^rt

A = 50000e^.0575(4)

= 51,163.33

 

The compound interest at 6% is better.

The difference in earnings is $12,285.95