Krishna saves Rs.24,000 a year for 5 years, and Rs.30,000 a year for 15 years thereafter. If the rate of interest is 9 % compounded annually, what will be the value of his savings at the end of 20 years?

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Your answer

To determine the value of Krishna's savings at the end of 20 years, we'll calculate the future value of the savings for the first 5 years and the subsequent 15 years separately, then sum them up. The interest rate is 9%, compounded annually.

### Step 1: Calculate the future value of savings for the first 5 years
For the first 5 years, Krishna saves Rs.24,000 annually. The future value of these savings at the end of 20 years can be calculated using the future value of an annuity formula:

\[
FV_1 = P \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- \( P = 24,000 \) (annual savings)
- \( r = 0.09 \) (annual interest rate)
- \( n = 5 \) (number of years of saving)

\[
FV_1 = 24,000 \times \frac{(1 + 0.09)^5 - 1}{0.09} = 24,000 \times \frac{(1.5386 - 1)}{0.09} = 24,000 \times 5.9844 = 143,625.6
\]

Now, this amount will grow for the remaining 15 years at 9% interest:

\[
FV_1' = FV_1 \times (1 + r)^{15} = 143,625.6 \times (1.09)^{15} = 143,625.6 \times 3.6425 \approx 522,903.39
\]

### Step 2: Calculate the future value of savings for the next 15 years
For the next 15 years, Krishna saves Rs.30,000 annually. The future value of these savings at the end of 20 years is:

\[
FV_2 = P \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- \( P = 30,000 \) (annual savings)
- \( r = 0.09 \)
- \( n = 15 \)

\[
FV_2 = 30,000 \times \frac{(1.09)^{15} - 1}{0.09} = 30,000 \times \frac{3.6425 - 1}{0.09} = 30,000 \times 29.3612 \approx 880,836
\]

### Step 3: Calculate the total future value at the end of 20 years
Now, add the future values from both periods:

\[
\text{Total Future Value} = FV_1' + FV_2 = 522,903.39 + 880,836 = 1,403,739.39
\]

### Final Answer:
The value of Krishna's savings at the end of 20 years will be approximately **Rs. 1,403,739.39**.

Would you like more details on any of these steps or have any other questions?

### Relative Questions:
1. What would be the savings value if the interest rate was 8% instead of 9%?
2. How would the final amount change if Krishna saved Rs.35,000 per year for the last 15 years?
3. What if Krishna started saving earlier and saved for 25 years instead of 20?
4. How does compounding frequency (e.g., semi-annually) affect the total savings?
5. What is the impact of withdrawing a portion of the savings midway through the period?

**Tip:** Always make sure to account for the compounding period when calculating the future value, as it significantly impacts the total amount accumulated over time.

Explore how to calculate the future value of savings with compound interest over 20 years. Detailed steps include computing the future value of annuities and compound interest at 9% annually. Discover the total savings value of Rs. 1,403,739.39.

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