Suppose you deposit $4900 into an account paying 0.025% simple daily interest and leave it there for one year. Assuming that you make no other deposits or withdrawals, how much will the account hold at the end of that time? Assume that a year is 365 days.
To calculate the amount the account will hold at the end of one year, we can use the formula for simple interest:
Simple Interest = Principal * Rate * Time
In this case, the principal is $4900, the rate is 0.025% (which is equivalent to 0.00025 as a decimal), and the time is 365 days.
First, we need to convert the rate to a daily rate. Since there are 365 days in a year, we divide the annual rate by 365:
Daily Interest Rate = 0.00025 / 365
Next, we calculate the simple interest for one day:
Simple Interest for One Day = $4900 * (0.00025 / 365)
Now, we need to multiply the daily interest by the number of days in a year to find the total interest earned over one year:
Total Interest = Simple Interest for One Day * 365
Finally, we can add the total interest to the principal to find the final amount in the account:
Final Amount = Principal + Total Interest
Let's calculate it step by step.
1. Calculate the daily interest rate:
Daily Interest Rate = 0.00025 / 365
2. Calculate the simple interest for one day:
Simple Interest for One Day = $4900 * (0.00025 / 365)
3. Calculate the total interest earned over one year:
Total Interest = Simple Interest for One Day * 365
4. Calculate the final amount in the account:
Final Amount = Principal + Total Interest
By following these steps, we can find out the exact amount the account will hold at the end of one year.