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
j = i/12 -- Monthly Interest Rate
r = 1+j -- Monthly Accumulation Factor
n = 18*12 = 216
p = The regular payment

The last payment will be ON the completion date. This payment will receive no interest.

p

The second to last payment will receive interest for one month,

pr

The third to last payment will receive interest for 2 months.

Thus: \(260000 = p(1 + r + r^{2} + ... + r^{n-1}) = p\dfrac{1-r^{n}}{1-r}\)

You're almost done. \(p = 260000\cdot\dfrac{1-r}{1-r^{n}}\)

Amount Deposited: 216 * p
Amount from Interest: 260000 - (216*p)

Answer 2

Is it 783.45 ?? @tkhunny

Answer 3

Is what 783.45?

Answer 4

That looks like the right payment. Now what?