A $2,000 deposit at an APR of 5.4% with quarterly compounding for 8 years. The amount after 8 years will be??
Enough already. By now if you are paying any attention you should be able to post at least an attempt at an answer.
rate is .054 /4
number of periods = 4*8 = 32
I did that and it said it was wrong I need the amount after 8 years how do I do that
.054/4 = .0135
that is your quarterly rate so every 3 months multiply by
1.0135
1.0135^32 = 1.53589
so multiply 2,000 by that. 3071.78
To find the amount after 8 years with quarterly compounding, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, the principal amount is $2,000, the annual interest rate is 5.4% (or 0.054 as a decimal), interest is compounded quarterly (n = 4), and the time period is 8 years (t = 8).
Plugging these values into the formula, we get:
A = 2000(1 + 0.054/4)^(4*8)
To solve this equation, we can break it down into smaller steps.
Step 1: Calculate (1 + 0.054/4)
This is equal to (1 + 0.0135) = 1.0135
Step 2: Calculate (4*8)
This is equal to 32
Step 3: Calculate (1.0135)^32
By raising 1.0135 to the power of 32, we get approximately 1.5987.
Step 4: Calculate 2000 * 1.5987
This gives us approximately $3,197.40.
Therefore, the amount after 8 years with quarterly compounding will be approximately $3,197.40.