# Geometric sequence help...

• May 3rd 2009, 08:18 AM
struck
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:

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

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 = $$\displaystyle 100,000 * 1.04^{25} ~= 266584 .. Dividing that by 25 gives 10,663 but that obviously isn't the answer. I have tried many other ways but I don't seem to get it (Surprised) • May 3rd 2009, 08:25 AM e^(i*pi) Quote: Originally Posted by struck A person wants to borrow 100,000 to buy a house. He intends to pay back a fixed sum of C at the end of each year, so that after 25 years he has completely paid off the debt. Assuming a steady interest rate of 4% per year, explain why: \displaystyle 100,000 = C(\frac{1}{1.04} + \frac{1}{1.04^2} + \frac{1}{1.04^3} + ... + \frac{1}{1.04^{25}}) I don't understand how is that even possible. If there's an interest rate of 4% per year, it should be a exponential growth, such that: Total payable sum =$$\displaystyle 100,000 * 1.04^{25}$~= 266584$ .. Dividing that by 25 gives $10,663 but that obviously isn't the answer. I have tried many other ways but I don't seem to get it (Surprised) Note that your first term is 1, your common ratio is 1/1.04 and there are 25 terms. From this you can use the sum of a geometric sequence:$\displaystyle S_{25} = \frac{1(\frac{1}{1.04})^{25}}{1.04-1}\$
• May 3rd 2009, 08:37 AM
struck
hmm .. I am trying to figure out how do you get the common ratio as 1/1.04.