Calculating Compound Amount of an Investment with Daily Compounding

How to calculate the compound amount of an investment with daily compounding?

To calculate the compound amount of an investment with daily compounding, you can use the compound interest formula modified as follows: - Rate per period (daily) = i ÷ 365 (nominal interest rate, i is divided by 365) - Number of periods (days), n, = a number of days of the investment The formula to calculate the compound amount is A = P(1+365i)^n. This formula takes into account the principal amount (P), nominal interest rate (i), and the number of days the investment is compounded daily (n).

Calculating Compound Amount of Thomas Ash's Account

Scenario: On April 18, Thomas Ash deposited $2,500 in a passbook savings account at 3.5% interest compounded daily.

Question: What is the compound amount (in $) of his account on August 5?

Final Answer: The compound amount on August 5 is $2,567.15.

Explanation: Thomas Ash's deposit of $2,500 at 3.5% interest compounded daily from April 18 to August 5 is calculated as follows: - Number of days from April 18 to August 5 = 109 days - Using the formula A = P(1+365i)^n: A = 2500(1 + (0.035/365))^109 A = $2,567.15 Therefore, the compound amount in Thomas Ash's account on August 5 is $2,567.15.

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