Answer: A
Step-by-step explanation:
Compound interest = P(1 + r/n)^nt
P = initial balance
r = annual interest rate
n = number of times the interest is compounded per year
t = number of years the money is invested
P= $20,000
n = 4
t = 1
Compound interest is greater than $21,000
21,000 = 20,000(1+r/4)^4
Divide both sides by 20,000, we have
1.05 = (1 + r/4)^4
Multiple both sides by the power of 1/4
(1.05)^ 1/4 = (1 + r/4)^ 4*1/4
1.01227= (1 +r/4)
Collect like terms
1.01227-1 = r/4
0.01227= r/4
r = 0.01227 * 4
r = 0.04908
r = 0.0491(approximate to 4 decimal places)
Recall that rate(r) is in percentage. Therefore multiply r by 100
0.0491*100
= 4.91%
4.91 is the least annual interest rate
