Math  /  Numbers & Operations

QuestionMilo is purchasing a new refrigerator for $2100\$ 2100 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 23.48%23.48 \%, how much would Milo owe on the 91st 91^{\text {st }} day if he made no payments during the first 90 days? Round your answer to the nearest cent, if necessary.

Studdy Solution

STEP 1

What is this asking? If Milo doesn't pay anything for 90 days, how much will he owe for the fridge, including interest? Watch out! The interest rate is *annual*, but we need it for 90 days, so we'll need to adjust it!

STEP 2

1. Calculate the daily interest rate.
2. Calculate the total interest.
3. Calculate the total amount owed.

STEP 3

We're given an *annual* interest rate of **23.48%**, which means for every $100\$100 borrowed for a year, Milo would owe $23.48\$23.48 in interest.
We need to figure out the *daily* rate, since the loan is for 90 days.

STEP 4

There are 365 days in a year, so to find the daily interest rate, we'll **divide** the annual rate by **365**.
This gives us the interest rate *per day*: 23.48%365=0.23483650.00064328767...\frac{23.48\%}{365} = \frac{0.2348}{365} \approx 0.00064328767... So, the daily interest rate is approximately **0.0006433**.

STEP 5

Now that we have the daily interest rate, we can **multiply** it by the **principal** (the initial amount borrowed, which is $2100\$2100) and the **number of days** (90) to find the total interest owed.
This is how much *extra* Milo will owe on top of the original price, just for borrowing the money.

STEP 6

Let's do the multiplication: 0.0006433$210090$121.280.0006433 \cdot \$2100 \cdot 90 \approx \$121.28 So, the total interest owed is approximately **\$121.28**.

STEP 7

To find the total amount Milo owes, we **add** the **original price** of the refrigerator and the **total interest**.
This gives us the grand total Milo has to pay.

STEP 8

Let's do the addition: $2100+$121.28=$2221.28\$2100 + \$121.28 = \$2221.28

STEP 9

Milo would owe approximately $2221.28\$2221.28 on the 91st day.

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