To solve this problem, we need to calculate the future value of the savings at the end of 10 years. The savings consist of two parts: Rs.5,000 per year for the first 3 years and Rs.7,000 per year for the next 7 years. The interest rate is 8%.

Step 1: Calculate the future value of Rs.5,000 saved annually for the first 3 years

The future value of an annuity can be calculated using the formula:

$FV = A \times \frac{(1 + r)^n - 1}{r}$

Where:

• $A = 5,000$ Rs.
• $r = 0.08$ (8% interest rate)
• $n = 3$ years

$FV_1 = 5,000 \times \frac{(1 + 0.08)^3 - 1}{0.08}$

$FV_1 = 5,000 \times \frac{1.259712 - 1}{0.08} = 5,000 \times 3.2464 \approx 16,232.01 \text{ Rs.}$

Step 2: Calculate the future value of Rs.16,232.01 at the end of 10 years

Since Rs.16,232.01 is accumulated at the end of 3 years, we need to calculate its value at the end of 10 years (which is 7 more years). This is done by compounding it forward:

$FV_1 (after 10 years) = 16,232.01 \times (1 + 0.08)^7$

$FV_1 (after 10 years) = 16,232.01 \times 1.71382 \approx 27,819.49 \text{ Rs.}$

Step 3: Calculate the future value of Rs.7,000 saved annually for the next 7 years

Now, calculate the future value of the Rs.7,000 saved annually for the next 7 years:

$FV_2 = 7,000 \times \frac{(1 + r)^n - 1}{r}$

Where:

• $A = 7,000$ Rs.
• $r = 0.08$ (8% interest rate)
• $n = 7$ years

$FV_2 = 7,000 \times \frac{(1 + 0.08)^7 - 1}{0.08}$

$FV_2 = 7,000 \times \frac{1.71382 - 1}{0.08} = 7,000 \times 8.92275 \approx 62,459.25 \text{ Rs.}$

Step 4: Add the future values to get the total savings at the end of 10 years

$Total \, Savings = FV_1 (after 10 years) + FV_2 = 27,819.49 \text{ Rs.} + 62,459.25 \text{ Rs.} \approx 90,278.74 \text{ Rs.}$

Final Answer:

The total savings at the end of 10 years will be approximately Rs.90,278.74.

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Would you like further details or have any questions?

Relative Questions:

1. What would be the future value if the interest rate was 10% instead of 8%?
2. How does the time period of savings affect the final accumulated amount?
3. What if you could save Rs.7,000 for all 10 years instead of Rs.5,000 for the first 3 years?
4. How would the savings cumulate if the interest was compounded monthly instead of annually?
5. What would happen if the savings started with Rs.7,000 for the first 7 years and Rs.5,000 for the last 3 years?

Tip:

When calculating future values of different savings or investments over time, break down the problem into parts and calculate the future value of each part separately before combining them.