**Answer:**

After **7.04 years **the amount will reach $57,000 or more

**Step-by-step explanation:**

The rule of the compound interest is , where

- n is the period of the time

∵ A loan of $36,000 is made at 6.75% interest, compounded annually

∴ **P = 36,000**

∴** r = **6.75% = 6.75 ÷ 100 = **0.0675**

∴ **n = 1** ⇒ compounded annually

∵ The amount after t years will reach $57,000 or more

∴ **A = 57,000**

→ To find t substitute these values in the rule above

∵ 57,000 = 36,000

∴ 57,000 = 36,000

→ Divide both sides by 36,000

∵ =

→ Insert ㏒ in both sides

∴ ㏒( ) = ㏒

→ Remember ㏒ = n ㏒()

∵ ㏒( ) = <em>t</em> ㏒(1.0675)

→ Divide both sides by ㏒(1.0675)

∴ 7.035151337 = <em>t</em>

<em>∴ </em>**<em>t </em>****≅ 7.04**

∴ **After 7.04 years the amount will reach $57,000 or more**