Suppose you deposit $400 in an account that earns 0.75 percent each quarter. You make no withdrawals from the account and deposit no more money into the account. How much money will accumulate after 2.5 years?
how about
400(1.075)^10 ?
or $824.41
At 0.75 percent, I don't think you'd more than double your money in just 2.5 years.
I got a different answer. I used 0.0075 as the multiplier and figured it the long way -- quarter by quarter.
In the first quarter you'd earn $3.00. Add that to the original 400 and again multiply by 0.0075. At the end of the second quarter, you'd have $406.02.
Finally, by the end of the 10th quarter, I got a total of $431.03.
of course!
I left out a zero, and then punched in that wrong value in my calculator, without thinking about the answer.
should have been
400(1.0075)^10
= 431.03
thanks for catching that
You're welcome, Reiny.
To find out how much money will accumulate after 2.5 years, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A is the total amount accumulated after t years,
P is the initial principal (starting amount),
r is the annual interest rate (expressed as a decimal),
n is the number of times interest is compounded per year, and
t is the number of years.
In this case:
P = $400 (initial deposit)
r = 0.75% = 0.0075 (0.75 percent as a decimal)
n = 4 (compounded quarterly)
t = 2.5 (2.5 years)
Now, we can substitute the values into the formula:
A = $400(1 + 0.0075/4)^(4*2.5)
Simplifying inside the parentheses:
A = $400(1 + 0.001875)^(10)
Calculating the exponent:
A = $400(1.001875)^(10)
Using a calculator, we find:
A ≈ $400(1.018886243)
A ≈ $407.55
Therefore, the amount of money that will accumulate after 2.5 years is approximately $407.55.