Question

An account is opened and 365 dollars are deposited at an annual

simple interest rate of 3.2%. At some later date, the total value
of the investment is $373. How many days had passed since the
account

Answer 1

Answer: 250

Explanation: To determine the number of days that had passed since the account was opened, we need to use the formula for simple interest:

Simple Interest = Principal × Interest Rate × Time

In this case, the principal is $365, the interest rate is 3.2% (or 0.032 as a decimal), and we're trying to find the time in days.

Let's assume the time in days is represented by "t". We can rearrange the formula to solve for "t" as follows:

Simple Interest = Total Value - Principal
Principal × Interest Rate × Time = Total Value - Principal
Interest Rate × Time = (Total Value - Principal) / Principal
Time = ((Total Value - Principal) / Principal) / Interest Rate

Now we can plug in the given values:

Total Value = $373
Principal = $365
Interest Rate = 0.032

Time = (($373 - $365) / $365) / 0.032

Calculating this expression:

Time = (8 / 365) / 0.032
Time = 8 / (365 × 0.032)
Time ≈ 8 / 11.68
Time ≈ 0.6849 years

Since we want to find the time in days, we can convert the time in years to days by multiplying by 365:

Time in days = 0.6849 × 365
Time in days ≈ 250.1935

Therefore, approximately 250 days had passed since the account was opened.