MATH SOLVE

2 months ago

Q:
# 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) 4.91B) 4.21C) 5.72D) 3.14E) 1.08

Accepted Solution

A:

Answer: AStep-by-step explanation:Compound interest = P(1 + r/n)^ntP = initial balance r = annual interest raten = number of times the interest is compounded per year t = number of years the money is invested P= $20,000n = 4t = 1Compound interest is greater than $21,00021,000 = 20,000(1+r/4)^4Divide both sides by 20,000, we have 1.05 = (1 + r/4)^4Multiple both sides by the power of 1/4(1.05)^ 1/4 = (1 + r/4)^ 4*1/41.01227= (1 +r/4)Collect like terms 1.01227-1 = r/40.01227= r/4r = 0.01227 * 4r = 0.04908r = 0.0491(approximate to 4 decimal places) Recall that rate(r) is in percentage. Therefore multiply r by 1000.0491*100= 4.91%4.91 is the least annual interest rate