A deposit account pays 4 % per annum with continuous compounding, but interest is actually paid

step 1 Okay, if you deposit $1 ,000 in an account in lifelong trust savings that pays 6 % interest comp

A deposit account pays 4 % per annum with continuous...

Key Concepts

Quarterly Interest Payment Calculation

To determine the interest paid each quarter on a deposit, one must first compute the effective quarterly interest rate from the continuous annual rate using the appropriate conversion formula and then multiply the resulting rate by the deposit amount. This method captures the actual interest earned during one quarter in a way that aligns with the compounding method specified.

Effective Interest Rate

The effective interest rate is the actual rate of interest earned or paid on an investment or loan over a period, taking into account the effects of compounding. It represents the true financial impact and is calculated by assessing the compounded growth over that specific period, rather than simply using the nominal rate.

Continuous Compounding

Continuous compounding refers to the process where interest is calculated and added to the principal an infinite number of times over a given period. In this context, the growth of an investment is modeled by the formula A = P × e^(rt), where P is the principal, r is the annual interest rate, t is the time in years, and e is the mathematical constant approximately equal to 2.71828.

Conversion from Continuous to Periodic Compounding

When dealing with a continuous interest rate that is paid out at discrete intervals (like quarterly), it is necessary to convert the annual continuous rate into an effective periodic rate. This conversion is achieved by using the formula for the effective rate over one period: effective rate = e^(r/n) - 1, where r is the annual continuous rate and n is the number of compounding periods per year.

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