Question

You would like to have $260,000 in 18 years by making regular deposits at the end of each month in an annuity that pays an annual interest rate of 4.5% compounded monthly. How much of the $260,000 comes from interest? In your calculations, do not round until the final answer. Then, round the monthly payment to the nearest dollar.

Answer 1

i = 0.045 -- Annual interest rate to be compounded monthly
j = i/12 = 0.00375 -- Monthly interest rate
r = 1+j = 1.00375 -- Monthly accumulation factor.

18*12 = 216

\(260000 = Pmt*(1 + r + r^2 + r^3 + ... + r^{215})\)

That's about it. Can you add the geometric series in the parentheses?

Answer 2

There is a formula for the monthly amount and it is attached.
monthly amount = 260,000 / [([((1.00375)^217)-1] / .00375)-1]
monthly amount = 260,000 / ((1.2529219598 / .00375)-1)
monthly amount = 260,000 / 333.1125226168
monthly amount = 780.52

Here is a calculator to double check that:
http://1728.org/annuitym.htm

Unfortunately this was all calculated with 4.5% annual interest and not with compounded monthly being taken into account.

Answer 3

Yes, there is a formula. There are several and it is often very hard to choose the right one. This is why I NEVER use one. I always build the correct formula from scratch and I never have to wonder if I have selected the right formula.

Unfortunately, @wolf1728 has selected the formula with payments at the BEGINNING of each month. Again, that's why I never use them. Too confusing.

You will want to start with the premise of the original problem statement. This leaves us with my question, Can you add the geometric series in the parentheses?