A $4000 deposit at an APR of 5.6% with a quarterly compounding for 8 years .
The amount after 8 years would be ???
OK, step by step
5.6 % = .056 yearly nominal
but it is quarterly/ so divide by 4
.014
so every three months, you multiply by
1.014
in other words add 1.4 percent of what you have to what you have every three months
Do this for 8 years which is 32 quarters
1.014 * 1.014 * 1.014 32 times
or
1.014^32 = 1.56032
so
4000 * 1.56032 = 6241.29
To find the amount after 8 years with a $4000 deposit at an Annual Percentage Rate (APR) of 5.6% compounded quarterly, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future amount
P = the principal amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $4000, the annual interest rate (r) is 5.6% (or 0.056 as a decimal), the compounding is quarterly (n = 4), and the time period (t) is 8 years.
Plugging in the values into the formula, we have:
A = $4000(1 + 0.056/4)^(4*8)
Simplifying:
A = $4000(1 + 0.014)^32
A = $4000(1.014)^32
A = $4000 * 1.497341797
A ≈ $5989.37
Therefore, the amount after 8 years would be approximately $5989.37.