Suppose you invest $1000 at an interest rate of 6%, compounded annually. Calculate the equivalent interest rate under continuous compounding (find the interest rate r that would give the same result if interest were compounded continuously). Hint: You can consider the situation for 1 year (let t=1).

The equivalent interest rate under continuous compounding is 5.8%

Explanation:

Annual compounding

A = P (1+r) ^n

P = $1,000

r = 6% = 0.06

n = 1 year

A = 1000 (1+0.06) ^1 = 1000 (1.06) = $1060

Continuous compounding

A = Pe^rt

A = $1060

P = $1000

t = 1 year

1060 = 1000e^r

e^r = 1060/1000 = 1.06

e^r = 1.06

r = ln 1.06 = 0.058 = 5.8%