A deposit in a bank, which pays interest on its deposits compounded daily, grows to Rs. 80,000 for 500 days and to 88,000 for 1000 days. What would be its value (in Rs.) for 1500 days?

Correct option is C

Given:
Amount after 500 days = ₹80,000
Amount after 1000 days = ₹88,000
Interest is compounded daily
Need to find the amount after 1500 days

Formula Used:
Compound Interest formula with daily compounding:

​$$A_t = P \cdot (1 + r)^t$$  

We use the ratio method for equal intervals:​

$$\frac{A_{t + \Delta}}{A_t} = (1 + r)^{\Delta}$$

Solution:
From the given:​

​$$\frac{A_{1000}}{A_{500}} = \frac{88000}{80000} = 1.1 \\\ \\\Rightarrow (1 + r)^{500} = 1.1\\\ \\A_{1500} = A_{1000} \cdot (1 + r)^{500}\\\ \\ = 88000 \cdot 1.1 = ₹96,800$$

Final Answer: (C) 96,800​