To solve this problem, we will use the formula for compound interest to find the future value of the investment and then solve for the amount $X$ that needs to be added to reach RM 40,000 in 5 years.

Step 1: Calculate the future value of the initial RM 15,000

The compound interest formula is: $A = P \left(1 + \frac{r}{n}\right)^{nt}$

Where:

• $A$ is the amount of money accumulated after n years, including interest.
• $P$ is the principal amount (the initial amount of money).
• $r$ is the annual interest rate (decimal).
• $n$ is the number of times that interest is compounded per year.
• $t$ is the time the money is invested for, in years.

Given:

• $P = 15,000$ RM
• $r = 0.055$ (5.5%)
• $n = 12$ (monthly compounding)
• $t = 5$ years

Substituting these values into the formula, we get: $A_1 = 15000 \left(1 + \frac{0.055}{12}\right)^{12 \times 5}$

$A_1 = 15000 \left(1 + 0.0045833\right)^{60}$

$A_1 = 15000 \left(1.0045833\right)^{60}$

$A_1 = 15000 \times 1.315475$

$A_1 = 19732.13$

Step 2: Calculate the additional amount needed to reach RM 40,000 in 5 more years

Let $X$ be the amount added now. This amount will also grow at the same interest rate and compounding period for the next 5 years. The future value of this additional amount is given by the same compound interest formula.

$A_2 = X \left(1 + \frac{0.055}{12}\right)^{12 \times 5}$

We need the sum of $A_1$ and $A_2$ to equal RM 40,000: $19732.13 + X \left(1.315475\right) = 40000$

Step 3: Solve for $X$

$X \left(1.315475\right) = 40000 - 19732.13$

$X \left(1.315475\right) = 20267.87$

$X = \frac{20267.87}{1.315475}$

$X \approx 15403.66$

Therefore, Sam needs to add approximately RM 15,403.66 to the account to have RM 40,000 in 5 years.

Would you like further details or have any questions?

Here are 5 related questions you might find interesting:

1. How does the frequency of compounding affect the future value of an investment?
2. What is the difference between compound interest and simple interest?
3. How can you calculate the time required to double an investment with a given interest rate?
4. How do changes in the interest rate impact the future value of an investment?
5. What are some common uses of compound interest in financial planning?

Tip: When dealing with compound interest, always remember to convert the interest rate to a decimal form by dividing the percentage by 100.