Aiman and Maya, are planning their savings for retirement. Both will save RM2,000 annually at an interest rate of 12% compounded annually. Maya starts at age 20 and deposits RM2,000 each year until age 29, making a total of 10 deposits. She then stops contributing and does nothing until retirement at age 65 (36 years of compound interest). Aiman starts at age 29 and deposits RM2,000 each year until retirement at age 65 (37 deposits). 
a)	How much will Maya have at age 65? (5 m)
b)	How much will Aiman have at retirement? (5 m)


This problem involves the concept of compound interest, where the future value of a series of annual deposits is calculated. 

We will calculate the future value for both Maya and Aiman using the formula for compound interest:

\[
FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \times (1 + r)^{T}
\]

Where:
- \(FV\) = future value
- \(P\) = annual deposit (RM 2,000)
- \(r\) = annual interest rate (12% or 0.12)
- \(n\) = number of years of deposits
- \(T\) = number of years remaining after the last deposit to retirement (for Maya, this applies)

### (a) Maya's Savings:

Maya deposits for 10 years, from age 20 to 29. After that, her money compounds for an additional 36 years without further contributions. So:

- Annual deposit \(P = 2,000\)
- Interest rate \(r = 0.12\)
- Number of deposits \(n = 10\)
- Number of years from last deposit to retirement \(T = 36\)

#### Step 1: Calculate the future value of Maya's 10 deposits at the end of year 29:

\[
FV_{Maya} = 2,000 \times \left( \frac{(1 + 0.12)^{10} - 1}{0.12} \right)
\]

#### Step 2: Compound Maya's savings for 36 more years:

After calculating the future value at age 29, we will then compound this value for 36 years at 12% interest.

\[
FV_{Maya_{final}} = FV_{Maya} \times (1 + 0.12)^{36}
\]

### (b) Aiman's Savings:

Aiman starts contributing at age 29 and makes 37 deposits, one each year until retirement at age 65. 

So, we will calculate his future value using the same formula but for 37 years of contributions:

\[
FV_{Aiman} = 2,000 \times \left( \frac{(1 + 0.12)^{37} - 1}{0.12} \right)
\]

Let me now calculate the future values for both Maya and Aiman.### (a) Maya's Savings at Age 65:
Maya will have approximately **RM 2,075,509.04** at age 65.

### (b) Aiman's Savings at Retirement:
Aiman will have approximately **RM 1,087,197.38** at age 65.

Though Maya only contributed for 10 years, the early start allowed her to accumulate significantly more savings compared to Aiman, who contributed for 37 years but started later. This illustrates the powerful effect of compound interest over time.

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Do you want further details or have any questions?

Here are five related questions:
1. How does compound interest differ from simple interest in savings calculations?
2. How would the final amounts change if the interest rate were lower, say 8% annually?
3. What is the effect of compounding more frequently, such as monthly, on the total amount saved?
4. How much would Maya have if she continued contributing after age 29?
5. What if Aiman started saving earlier, at the same age as Maya?

**Tip**: Starting to save earlier can have a much greater impact than increasing the amount saved each year!

Aiman and Maya, are planning their savings for retirement. Both will save RM2,000 annually at an interest rate of 12% compounded annually. Maya starts at age 20 and deposits RM2,000 each year until age 29, making a total of 10 deposits. She then stops contributing and does nothing until retirement at age 65 (36 years of compound interest). Aiman starts at age 29 and deposits RM2,000 each year until retirement at age 65 (37 deposits). a) How much will Maya have at age 65? b) How much will Aiman have at retirement?

Calculate the future value of retirement savings for Aiman and Maya with annual contributions of RM2,000 at a 12% compounded annual interest rate. Maya starts at age 20 and stops after 10 years, allowing the compound interest to grow for 36 more years, while Aiman starts at age 29 and continues until age 65. Learn about the impact of early savings and compound interest on retirement planning. Suitable for high school students studying finance and mathematics.

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