 If GH¢300,000 is to be saved over 25 years, how much should be deposited monthly if the investment eams 8% interest compounded monthly?

To solve this problem, we can use the formula for the future value of an annuity, which accounts for regular deposits into an account earning compound interest. The formula is:

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

Where:
- \(FV\) is the future value of the investment, which is GH¢300,000.
- \(P\) is the monthly deposit (the amount we need to find).
- \(r\) is the monthly interest rate.
- \(n\) is the total number of payments (total number of months).

### Step 1: Identify the values

- \(FV = 300,000\)
- Annual interest rate \( = 8\% \), so the monthly interest rate \(r = \frac{8\%}{12} = \frac{0.08}{12} \approx 0.00667\).
- The number of years is 25, so the total number of months \(n = 25 \times 12 = 300\).

### Step 2: Rearrange the formula to solve for \(P\)

We need to solve for \(P\), so rearrange the formula:

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

### Step 3: Plug in the values and calculate

\[
P = \frac{300,000 \times 0.00667}{(1 + 0.00667)^{300} - 1}
\]

Let me calculate this for you.The amount that should be deposited monthly is approximately **GH¢315.45** to save GH¢300,000 over 25 years at an 8% interest rate compounded monthly.

Would you like more details, or do you have any other questions?

### Related Questions
1. How does the interest rate affect the monthly deposit amount?
2. What if the interest is compounded quarterly instead of monthly?
3. How would the required monthly deposit change if the goal was GH¢500,000 instead?
4. How can you calculate the total interest earned over the 25 years?
5. What is the difference between simple interest and compound interest?
6. How do changes in the deposit period (e.g., 20 years instead of 25) affect the monthly deposit?
7. What if the deposit frequency was yearly instead of monthly?
8. How can inflation impact the future value of the savings?

### Tip
When dealing with compound interest, remember that the frequency of compounding (monthly, quarterly, annually) significantly impacts the amount of interest accrued over time.

Learn how to calculate the monthly deposit required to save GH¢300,000 over 25 years at an 8% interest rate compounded monthly. Understand the Future Value of Annuity formula and its application in financial planning.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation