You decide to make regular deposits every month into an account that earns 3% annual interest, compounded monthly. You hope to have $28000 at the end of 22 years. What is the amount of the regular payment you need to make?
help
This, like your previous post, is a direct application of the basic formula.
You MUST know these formulas.
amount = paym( (1+i)^n - 1)/i
for yours: i = .03/12 = .0025 , n = 22*12 = 264
paym( 1.0025^264 - 1)/.0025 = 28000
solve for paym
let me know what you get, to make sure you understand how to calculate this.
What would the final answer be?
I want YOU to do it. Good grief, I gave you the method.
Giving you the "answer" will teach you absolutely nothing, and you will have
learned nothing.
would this be correct?
373.27977686
=
28000
Nope,
How did you possible get that ???
To determine the amount of the regular payment you need to make, we can use the formula for the future value of an ordinary annuity:
FV = P * (((1 + r)^n - 1) / r)
Where:
FV = Future value of the annuity ($28,000 in this case)
P = Regular payment amount
r = Interest rate per period (3% per year = 0.03/12 per month)
n = Number of periods (22 years = 22 * 12 months)
Let's substitute the given values into the formula and solve for P:
28000 = P * (((1 + 0.03/12)^(22*12)) - 1) / (0.03/12)
First, simplify the exponent:
28000 = P * (((1 + 0.0025)^(264)) - 1) / 0.0025
Next, calculate the expression in parentheses:
28000 = P * ((1.0025^(264)) - 1) / 0.0025
Finally, isolate P by multiplying both sides by 0.0025 and dividing by ((1.0025^(264)) - 1):
P = 28000 * 0.0025 / ((1.0025^(264)) - 1)
Using a calculator, evaluate the expression to find the value of P:
P ≈ $70.78 (rounded to two decimal places)
Therefore, the amount of the regular payment you need to make is approximately $70.78.