Five years ago Sam had saved RM 15,000 in an account that pays 5.5% compounded monthly. Now he intended to add another RMX into truss same account. Find the value of x of the account will amount too RM 40,000 in 5 years.

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.

Learn how to solve a compound interest problem where Sam aims to reach RM 40,000 in 5 years with an initial investment of RM 15,000 at 5.5% annual interest compounded monthly. Calculate the additional amount needed and understand compound interest concepts. Suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation