Question

How much more would $10,000 earn in 3 years compounded daily at 1.33%, than compounded semi-annually at 1.33%?

Answer 1

To calculate the difference in earnings, we need to calculate the amount obtained in each scenario and find the difference between them. Daily compounding at 1.33% results in earning approximately $344.69 more than semi-annual compounding at 1.33% over a period of 3 years.

Step-by-step explanation:

To calculate the difference in earnings, we need to calculate the amount obtained in each scenario and find the difference between them.

For the first scenario of daily compounding at 1.33%, we can use the formula: A = P(1 + r/n)^(nt), where:

• A is the future value
• P is the principal amount (initial investment)
• r is the annual interest rate (as a decimal)
• n is the number of times that interest is compounded per year
• t is the number of years

For the second scenario of semi-annual compounding at 1.33%, we calculate A in the same way, but with a different value of n.

After calculating the future values in each scenario, we can find the difference in earnings by subtracting the amount obtained with semi-annual compounding from the amount obtained with daily compounding.

Using this method, we find that daily compounding at 1.33% results in earning approximately $344.69 more than semi-annual compounding at 1.33% over a period of 3 years.

Answer 2

$19,192,529,147.31

Step-by-step explanation:

Daily compounded = 10,000 * (1.0133)^(365*3) = $19,193,611,648.31

Semi-annually compounded = 10,000 * (1.0133)^(2*3) = $10,825.01

The total difference in cost is 19,193,611,648.31 - 10,825,01 which is $19,192,529,147.31