How much money did Lana borrow, if the amount to be paid in 6 months with simple monthly 4% accrual was 620 GEL?

To find out how much Lana borrowed, we can use the formula for simple interest:

\[
A = P(1 + rt)
\]

Where:
- \(A\) is the final amount to be paid (620 GEL),
- \(P\) is the principal amount (the money Lana borrowed),
- \(r\) is the interest rate per time period (monthly rate of 4% or 0.04),
- \(t\) is the time period in months (6 months).

We need to solve for \(P\), the amount borrowed:

\[
620 = P(1 + 0.04 \times 6)
\]

Simplifying the equation:

\[
620 = P(1 + 0.24) \quad \Rightarrow \quad 620 = P(1.24)
\]

Solving for \(P\):

\[
P = \frac{620}{1.24} \quad \Rightarrow \quad P = 500 \, \text{GEL}
\]

Thus, Lana borrowed **500 GEL**.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. What would be the interest paid in this case?
2. How would the formula change if the interest was compounded monthly?
3. What if Lana borrowed the money for a year at the same interest rate?
4. How much would Lana need to pay if the interest rate was 5% monthly?
5. What happens to the total payment if the borrowing time is doubled?

**Tip:** Always ensure the time period and interest rate correspond (monthly, yearly, etc.) for accurate calculations.

Find out how much Lana borrowed with 4% simple interest over 6 months, using the simple interest formula A = P(1 + rt). In this problem, Lana needs to pay 620 GEL at the end of 6 months. Learn how to calculate the principal amount, suitable for students in Grades 8-10.

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