Question

Your bank is offering a savings account with a nominal rate of 1.5%, compounded continuously. If you deposit $1,000 in 2010, what will your balance be in 2020? What is the effective annual yield?

Answer 1

$1,161.83

1.51%

Explanation:

Continuously compounded interest is:

A = Pe^(rt)

where A is the final amount,

P is the initial amount,

r is the rate per time,

and t is time.

Given P = 1000, r = 0.015, and t = 10:

A = 1000e^(0.015 × 10)

A = 1000e^(0.15)

A = 1161.83

The effective annual yield is the annually compounded rate needed to have the same yield after the same time. For continuously compounded interest, he equation for effective annual yield is:

R = -1 + e^r

R = -1 + e^0.015

R = 0.0151

The effective annual yield is 1.51%.