Answer:
4.86%
Step-by-step explanation:
You want the interest rate compounded annually that increases a deposit of $3000 to $3804 in 5 years.
The balance in an account earning compounded interest is given by ...
A = P(1 +r)^t
where P is the amount invested at rate r for t years.
Filling in the given values, we have ...
3804 = 3000(1 +r)^5
1.268 = (1 +r)^5 . . . . . . . . . divide by 3000
(1.268)^(1/5) = 1 +r . . . . . . take 5th root
r = 1.268^(1/5) -1 ≈ 1.048634 -1 ≈ 4.86%
The account earns about 4.86% interest annually.
Answer:
26.8%
Step-by-step explanation:
To find the interest rate, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (3804 in this case)
P = the principal amount (3000 in this case)
r = the interest rate
n = the number of times interest is compounded per year (annually in this case)
t = the number of years (5 in this case)
Let's rearrange the formula to solve for r:
r = ( (A/P)^(1/(n*t)) - 1 ) * n
Plugging in the values:
r = ( (3804/3000)^(1/(1*5)) - 1 ) * 1
Calculating the expression:
r = (1.268 - 1) * 1
r = 0.268
Therefore, the interest rate for the $3000 deposit accumulating to $3804, compounded annually for 5 years, is approximately 26.8%.
