# Thread: Geometric sequence help...

1. ## Geometric sequence help...

A person wants to borrow $100,000 to buy a house. He intends to pay back a fixed sum of$C at the end of each year, so that after 25 years he has completely paid off the debt. Assuming a steady interest rate of 4% per year, explain why:

$100,000 = C(\frac{1}{1.04} + \frac{1}{1.04^2} + \frac{1}{1.04^3} + ... + \frac{1}{1.04^{25}})$

I don't understand how is that even possible. If there's an interest rate of 4% per year, it should be a exponential growth, such that:

Total payable sum = $$100,000 * 1.04^{25}$ ~= 266584$ .. Dividing that by 25 gives $10,663 but that obviously isn't the answer. I have tried many other ways but I don't seem to get it 2. Originally Posted by struck A person wants to borrow$100,000 to buy a house. He intends to pay back a fixed sum of $C at the end of each year, so that after 25 years he has completely paid off the debt. Assuming a steady interest rate of 4% per year, explain why: $100,000 = C(\frac{1}{1.04} + \frac{1}{1.04^2} + \frac{1}{1.04^3} + ... + \frac{1}{1.04^{25}})$ I don't understand how is that even possible. If there's an interest rate of 4% per year, it should be a exponential growth, such that: Total payable sum =$ $100,000 * 1.04^{25}$ ~= 266584$.. Dividing that by 25 gives$10,663 but that obviously isn't the answer.

I have tried many other ways but I don't seem to get it
Note that your first term is 1, your common ratio is 1/1.04 and there are 25 terms.

From this you can use the sum of a geometric sequence:

$S_{25} = \frac{1(\frac{1}{1.04})^{25}}{1.04-1}$

3. hmm .. I am trying to figure out how do you get the common ratio as 1/1.04.