A college student expects to earn at least $1,000 in interest on an initial investment of $20,000. If the money is invested for one year at interest compounded quarterly, what is the least annual interest rate that would achieve the goal?

A) 4.91

B) 4.21

C) 5.72

D) 3.14

E) 1.08

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