Ann deposited $4000 into an account with 5.2 interest, compounded quarterly. Assuming that no withdrawals are made, how much will she have in the account after 3 years?
P=principal ($4000) or present value
r=interest rate per period (5.2% p.a.= 1.3% per quarter)
n=number of periods (3*4 quarters = 12)
Amount after 3 years (future value)
=P(1+r)^n
=4000(1.013)^12
= ?
Chris deposited $4,000 into an account with 2.6% interest, compounded quarterly. Assuming that no withdrawals are made how much will he have in the account after 4 years?
Well, since Ann deposited $4000 into an account, I hope she remembered to get a receipt. Can't have those hard-earned dollars disappearing, right? Now, let's get calculating.
If the interest is 5.2%, compounded quarterly, we need to first figure out the quarterly interest rate. So, we divide 5.2% by 4 because there are 4 quarters in a year.
That gives us a quarterly interest rate of 1.3%. Now, let's use the magic of compounding interest to find out how much Ann will have after 3 years.
After the first quarter, Ann's balance will be $4000 + ($4000 * 1.3%).
After the second quarter, Ann's balance will be [previous balance] + ([previous balance] * 1.3%).
And we continue this cycle for 12 quarters since we're calculating over 3 years.
So, pull out your calculator, and let's start multiplying and adding those numbers. But remember, no funny business with the decimals, okay?
After all the calculations are done, Ann should have a whopping amount in her account. Just don't forget to tell her to take her clown advisor out for a fancy dinner with some of that money!
To find out how much Ann will have in the account after 3 years with compound interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money after the specified time period
P = the principal amount (initial deposit)
r = the interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, Ann deposited $4000, the interest rate is 5.2% or 0.052 as a decimal, the interest is compounded quarterly, which means n = 4 (since there are 4 quarters in a year), and the time period is 3 years.
Plugging the values into the formula:
A = 4000(1 + 0.052/4)^(4*3)
Now, let's simplify the equation step by step:
A = 4000(1 + 0.013)^12
A = 4000(1.013)^12
A = 4000(1.1774)
Now, we can calculate the final amount Ann will have in the account after 3 years:
A ≈ $4709.60
Therefore, Ann will have approximately $4709.60 in the account after 3 years, assuming no withdrawals are made.