Question

A. Use the formula for continuous compounding with the original example: $1000 invested at 2% for 1 year. Record the amount to 5 decimal places. Use a calculator.
B. Compare it to the result using the original compound interest formula with n = 365 calculated to 5 decimal places. Which has a larger value? Explain.

Answer 1

Hi there

Continuous compounding
1) A=1,000×e^(0.02×1)
=1,020.20134...larger value

Daily compounding
2) A=1,000×(1+0.02÷365)^(365×1)
=1,020.20078

Continuous compounding is larger
1,020.20134−1,020.20078
=0.00056

Reason
The effect of compound interest depends on frequency.Continuously compounded returns compound the most frequently of all because the interest with continuously compounded is computed every second while the interest with daily compounding is computed every day

Hope it helps