Milo is purchasing a new refrigerator for $3300
$
⁢
3300
using an in-store offer. The store is offering a 90
90
days same-as-cash loan. This means that at the end of the 90
90
days, if Milo has paid off the cost of the refrigerator, he owes no added interest charge, but if he does not pay off the entire cost of the refrigerator, he owes simple interest on the original purchase amount, calculated over the entire 90
90
days. If the annual interest rate is 15.12%
15.12
%
, how much would Milo owe on the 91st
91
st
day if he made no payments during the first 90
90
days? Round your answer to the nearest cent, if necessary.

To solve this problem, we need to calculate how much Milo will owe on the 91st day if he makes no payments during the first 90 days. Since the interest is applied as simple interest on the original purchase amount, we'll use the simple interest formula:

\[
I = P \times r \times t
\]

Where:
- $ I $ is the interest,
- $ P $ is the principal (original amount),
- $ r $ is the annual interest rate (as a decimal),
- $ t $ is the time in years.

### Step 1: Convert the time to years
The time given is 90 days, but the interest rate is annual, so we need to express 90 days as a fraction of a year. Since there are 365 days in a year:

\[
t = \frac{90}{365}
\]

### Step 2: Convert the interest rate to a decimal
The annual interest rate is given as 15.12%. Converting this to a decimal:

\[
r = \frac{15.12}{100} = 0.1512
\]

### Step 3: Calculate the interest
Now, we calculate the interest using the formula. The principal $ P $ is \$3,300:

\[
I = 3300 \times 0.1512 \times \frac{90}{365}
\]

Let's compute the interest.The interest Milo would owe after 90 days is approximately \$123.03.

### Step 4: Calculate the total amount owed
On the 91st day, Milo will owe the original principal plus the interest:

\[
\text{Total amount owed} = P + I = 3300 + 123.03 = 3423.03
\]

Thus, Milo would owe **\$3423.03** on the 91st day if he made no payments during the first 90 days.

Would you like more details on any part of this calculation?

Here are five related questions to expand your understanding:
1. How would the amount owed change if the interest rate was higher?
2. What if Milo paid off half the refrigerator price within the 90 days?
3. How is simple interest different from compound interest in such loans?
4. What would the total amount owed be if the loan period was extended to 120 days?
5. How would the calculation change if the store offered monthly interest instead of annual interest?

**Tip:** Always check whether interest is compounded or simple when analyzing loan agreements, as it can significantly affect the total cost!

Milo is purchasing a new refrigerator for $3300 using an in-store offer. The store is offering a 90 days same-as-cash loan. This means that at the end of the 90 days, if Milo has paid off the cost of the refrigerator, he owes no added interest charge, but if he does not pay off the entire cost of the refrigerator, he owes simple interest on the original purchase amount, calculated over the entire 90 days. If the annual interest rate is 15.12%, how much would Milo owe on the 91st day if he made no payments during the first 90 days? Round your answer to the nearest cent, if necessary.

Learn how to calculate the simple interest on a $3300 purchase with a 90-day same-as-cash loan and a 15.12% annual interest rate. See how Milo's total amount due on the 91st day comes to $3423.03, covering key financial concepts like interest rate conversion and time adjustments. Suitable for students in Grades 9-11.

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