A loan of $36,000 is made at 6.75% interest, compounded annually. After how many years will the amount due reach $57,000 or more?

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

Step-by-step explanation:

The rule of the compound interest is , where

∵ 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 ㏒()

∵ ㏒( ) = t ㏒(1.0675)

→ Divide both sides by ㏒(1.0675)

∴ 7.035151337 = t

∴ t ≅ 7.04

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

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