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

\[A=P(1+\frac{ r }{ n })^{r \times t}\]

Answer 2

I got that! i have $783.44 but i dont know how to find the interest

Answer 3

Yea, no. That's for a single payment only. You have regular, periodic payments.

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.

P = The regular Payment
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

There's all the building blocks you need. Now what?

Answer 4

I just dont know what the question is asking for?

Answer 5

It's first asking for P.

n = 1 and P = 1000

n*P = 1000 -- Just one payment at the end of the single period.

n = 2 and P = 1000

1000 + 1.00375(1000) = 2003.75

n = 3 and P = 1000

1000 + 1.00375(1000) + 1.00375^2[1000] = 3011.2640625

n = 4 and P = 1000

1000 + 1.00375(1000) + 1.00375^2[1000] + 1.00375^3[1000] = 4022.55630273

You need to keep doing this until you get n all the way up to 216.

THEN, you have to get the right payment. $1,000 is not the right answer.