Linda's grandmother deposits an amount into a bank account at Linda's birth. The function y=2000-1.0425 describes how much money, SEK y, is in the bank account x years later. How much money would be in Linda's account on her 8th birthday if the interest rate after 5 years was changed to 3.5%?

The function provided, \( y = 2000 - 1.0425^x \), describes the amount of money in the bank account \( y \) SEK as a function of \( x \) years after the initial deposit. This function appears to describe a compound interest scenario with an initial principal amount of 2000 SEK, but it is expressed in a slightly unconventional form.

However, since the problem involves a change in interest rate after 5 years, we need to calculate the amount in two stages:

### Stage 1: First 5 Years (1.0425% Interest Rate)
- For the first 5 years, the interest rate is 1.0425% per year.
- The amount after 5 years can be calculated using the original formula.

### Stage 2: Remaining 3 Years (3.5% Interest Rate)
- After the 5th year, the interest rate changes to 3.5%.
- We will calculate the compound interest for the next 3 years using the new rate.

### Calculations

#### 1. Calculate the amount after 5 years:
\[
y(5) = 2000 \times 1.0425^5
\]

#### 2. Calculate the amount after 8 years with the new interest rate:
- First, determine the amount after 5 years (which becomes the new principal).
- Then, calculate the compound interest for the next 3 years using 3.5% as the new rate.

\[
y(8) = y(5) \times 1.035^3
\]

Let's compute these values.The amount in Linda's bank account on her 8th birthday would be approximately **2730.43 SEK**.

Would you like further details or have any other questions?

Here are some related questions:
1. How does compound interest differ from simple interest?
2. What happens to the total amount if the interest rate is increased after a certain period?
3. How do you calculate the effective annual rate (EAR) from a nominal interest rate?
4. What are some common interest rate formulas for different compounding periods?
5. How would the final amount change if the interest rate decreased after 5 years instead?
6. What is the effect of compounding frequency on the final amount?
7. How do you determine the time required to double an investment with a given interest rate?
8. What role does inflation play in the real value of the amount in a bank account over time?

**Tip:** When dealing with varying interest rates, always break down the time periods and calculate the amount step by step to ensure accuracy.

Explore how compound interest affects Linda's bank account balance as her grandmother deposits an amount using a changing interest rate. Calculate the amount on Linda's 8th birthday with step-by-step compound interest calculations.

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