suppose you have 11000 to invest which of the two rates woul

suppose you have $11,000 to invest. which of the two rates would yield the larger amount in 4 years: 8% compounded monthly or 7.91% compounded continuously?

8% compounded monthly
7.91% compounded continuously

Solution

8% monthly :

A = P(1 + r)^t

P = 11000
r = 8/12 = 2/3% = 2/300 = 1/150
t = 4 yrs * 12 = 48 periods

So, we have
A = 11000(1 + 1/150)^48
A = 15132.33

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7.91% continuously :
r = 0.0791

A = P*e^(rt)

A = 11000 * e^(0.0791*4)
A = 15093.97

So, we get a larger turnover from 8% monthly!